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Robustness of interdependent directed higher-order networks against cascading failures Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-03-10 Dandan Zhao, Xianwen Ling, Hao Peng, Ming Zhong, Jianmin Han, Wei Wang
In the real world, directed networks are not just constructed as pairs of directed interactions, but also occur in groups of three or more nodes that form the higher-order structure of the network. From social networks to biological networks, there is growing evidence that real-world systems connect the functional relationships of multiple systems through interdependence. To understand the robustness
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Homogeneous and heterogeneous nucleation in the three-state Blume–Capel model Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-03-05 Emilio N.M. Cirillo, Vanessa Jacquier, Cristian Spitoni
We study metastability in a three-state lattice spin system in presence of zero-boundary condition, which is a relevant choice from the point of view of applications, since it mimics the presence of defects in the system. This problem is studied in the framework of the stochastic Blume–Capel model with Glauber dynamics and it is proven that the presence of zero-boundary conditions changes drastically
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On behavior analysis of solutions for the coupled higher-order WKI equation Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-03-02 Xianguo Geng, Wenhao Liu
A coupled higher-order WKI equation is proposed and its 4 × 4 matrix Lax pair is derived. On the basis of spectral analysis of the 4 × 4 matrix spectral problems related to the coupled higher-order WKI equation, the basic Riemann–Hilbert problem is established by using the inverse scattering transformation. Resorting to the nonlinear steepest descent method, the solution of the basic Riemann–Hilbert
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Jointly equivariant dynamics for interacting particles Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-03-02 Alain Ajami, Jean-Paul Gauthier, Francesco Rossi
Let a finite set of interacting particles be given, together with a symmetry Lie group . Here we describe all possible dynamics that are jointly equivariant with respect to the action of . This is relevant e.g., when one aims to describe collective dynamics that are independent of any coordinate change or external influence.
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Pollution overturning instability in an incompressible fluid with a Maxwell-Cattaneo-Mariano model for the pollutant field Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-03-01 Martina Nunziata, Vincenzo Tibullo
We develop a model for a pollutant dissolved in or dispersed in an incompressible Navier–Stokes fluid when the diffusion theory for the pollutant obeys a second order in time system of equations rather than the first order in time system obtained from Fourier’s law. A detailed analysis is performed for a layer of fluid where a pollutant is such that the top of the layer will be in concentration. A
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Perturbing masses: A study of centered co-circular central configurations in power-law n-body problems Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-03-01 Zhengyang Tang, Shuqiang Zhu
This research investigates centered co-circular central configurations in the general power-law potential -body problem. Firstly, there are no centered co-circular central configurations exist when precisely of the masses are equal; secondly, unless all masses are equal, no such configurations exist when masses can be divided into two sets of equal masses; thirdly, no such configurations exist when
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Conditions on feature lines of two-dimensional scalar fields and their application to planar fluid flows Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-29 Balázs Sándor, Péter Torma
We give a local algebraic condition on the coincidence of feature lines of contour curvature and slope (the latter is associated with ridges and valleys in a terrain map) for general two-dimensional scalar fields employing two newly derived feature lines. We also give a sufficient condition on the coincidence of feature lines using the reflection symmetries of the contour curves. We analyze the coincidence
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On the correspondence between symmetries of two-dimensional autonomous dynamical systems and their phase plane realisations Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-29 Fredrik Ohlsson, Johannes G. Borgqvist, Ruth E. Baker
We consider the relationship between symmetries of two-dimensional autonomous dynamical systems in two common formulations; as a set of differential equations for the derivative of each state with respect to time, and a single differential equation in the phase plane representing the dynamics restricted to the state space of the system. Both representations can be analysed with respect to their symmetries
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On the dynamical Rayleigh–Taylor instability of 2D inviscid geophysical fluids with geostrophic balance Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-28 Yiqiu Mao, Quan Wang, Chao Xing, Liang Yang
We investigate the nonlinear instability of a steady-state solution to the two-dimensional nonhomogeneous incompressible Euler equations. The solution has a smooth, steady density profile and a background shear, which is derived from the balance of a uniform gravitational field, Coriolis forcing, and pressure. The density profile is characterized by an increasing heavier density with height, which
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Rogue waves and their patterns for the coupled Fokas–Lenells equations Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-28 Liming Ling, Huajie Su
In this work, we explore the rogue wave patterns in the coupled Fokas–Lenells equation by using the Darboux transformation. We demonstrate that when one of the internal parameters is large enough, the general high-order rogue wave solutions generated at a branch point of multiplicity three can be decomposed into some first-order outer rogue waves and a lower-order inner rogue wave. Remarkably, the
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Symplectic Grothendieck polynomials, universal characters and integrable systems Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-27 Fang Huang, Chuanzhong Li
This paper is concerned with the K-theoretic analogs of symplectic Schur functions and symplectic universal character. In this paper, we first show that the linear transformations of the vertex operators presentation of symplectic Schur functions are polynomial tau-functions of symplectic KP hierarchy, and give a new symmetric function called symplectic Grothendieck polynomial, together with its vertex
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Intermittent phase dynamics of non-autonomous oscillators through time-varying phase Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-23 Julian Newman, Joseph P. Scott, Joe Rowland Adams, Aneta Stefanovska
Oscillatory dynamics pervades the universe, appearing in systems of all scales. Whilst autonomous oscillatory dynamics has been extensively studied and is well understood, the very important problem of non-autonomous oscillatory dynamics is less well understood. Here, we provide a framework for non-autonomous oscillatory dynamics, within which we can define intermittent phenomena such as intermittent
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Orbital stability of periodic traveling waves in the b-Camassa–Holm equation Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-22 Brett Ehrman, Mathew A. Johnson
In this paper, we identify criteria that guarantees the nonlinear orbital stability of a given periodic traveling wave solution within the b-family Camassa–Holm equation. These periodic waves exist as 3-parameter families (up to spatial translations) of smooth traveling wave solutions, and their stability criteria are expressed in terms of Jacobians of the conserved quantities with respect to these
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Well-posedness and limit behavior of stochastic fractional Boussinesq equation driven by nonlinear noise Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-22 Shang Wu, Jianhua Huang
This paper primarily explores the well-posedness and limit behavior of the stochastic fractional Boussinesq equation driven by periodic force and nonlinear noise. Firstly, we establish the existence and uniqueness of the strong solution in probabilistic sense. Subsequently, the existence of weak mean random attractor and evolution systems of measures will be proved. Furthermore, we investigate the
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The evolving butterfly: Statistics in a changing attractor Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-22 Gosha Geogdzhayev, Andre N. Souza, Raffaele Ferrari
The Earth system is often modeled as a dynamical system in what has come to be known as Earth Systems Models. When used to study anthropogenically forced climate change, these models are forced in such a way that they are not in a statistically stationary state. Yet, statistical statements are still made about the Earth system using only a single trajectory by taking temporal averages. At each moment
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Distributed control of partial differential equations using convolutional reinforcement learning Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-21 Sebastian Peitz, Jan Stenner, Vikas Chidananda, Oliver Wallscheid, Steven L. Brunton, Kunihiko Taira
We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs). Exploiting translational equivariances, the high-dimensional distributed control problem can be transformed into a multi-agent control problem with many identical, uncoupled
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Nonintegrability of dissipative planar systems Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-21 Kazuyuki Yagasaki
We consider dissipative autonomous perturbations of planar Hamiltonian systems and give a sufficient condition for them not to be complex-meromorphically Bogoyavlenskij-integrable such that the first integral or commutative vector field also depends complex-meromorphically on the small parameter. We illustrate the theoretical result for three examples including systems with the Morse potential and
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On the Fredholm determinant of the confluent hypergeometric kernel with discontinuities Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-21 Shuai-Xia Xu, Shu-Quan Zhao, Yu-Qiu Zhao
We consider the determinantal point process with the confluent hypergeometric kernel. This process is a universal point process in random matrix theory and describes the distribution of eigenvalues of large random Hermitian matrices near the Fisher-Hartwig singularity. Applying the Riemann-Hilbert method, we study the generating function of this process on any given number of intervals. It can be expressed
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On the dynamics of predator–prey models with role reversal Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-21 Purnedu Mishra, Arcady Ponosov, John Wyller
We present a novel mathematical model that incorporates role reversal in predator–prey interactions. In particular, we consider the case where adult preys attack and kill juvenile predators. The model is derived from the McKendrick–Von Foerster equation and includes a maturation delay for juvenile predators. We prove that the initial value problem of the modeling framework is globally wellposed and
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Finite difference methods for nonlinear fractional differential equation with [formula omitted]-Caputo derivative Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-20 Changpin Li, N’Gbo N’Gbo, Fang Su
In this article, we construct finite difference methods for nonlinear fractional differential equation with -Caputo derivative. The rectangle, interpolation, and predictor–corrector methods on non-uniform meshes are proposed. The numerical stability analysis and error estimates are displayed. Numerical examples are also given to illustrate the theoretical results, where the chaotic attractors in the
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The quasi-periodic solution of fractional nonlinear Schrödinger equation on tori Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-19 Jieyu Liu, Jing Zhang
This paper is concerned with the fractional nonlinear Schrödinger equation with periodic boundary conditions where , and is a real analytic function in some neighborhood of the origin in . The above equation (0.1) is reversible with respect to the involution . By the KAM (Kolmogorov–Arnold–Moser) theorem for an infinite dimensional reversible system with unbounded perturbation, we obtain that there
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Characterisations for the depletion of reactant in a one-dimensional dynamic combustion model Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-17 Siran Li, Jianing Yang
In this paper, a novel observation is made on a one-dimensional compressible Navier–Stokes model for the dynamic combustion of a reacting mixture of -law gases () with a discontinuous Arrhenius reaction rate function, on both bounded and unbounded domains. We show that the mass fraction of the reactant (denoted as ) satisfies a weighted gradient estimate , provided that at time zero the density is
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Data-driven model selections of second-order particle dynamics via integrating Gaussian processes with low-dimensional interacting structures Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-16 Jinchao Feng, Charles Kulick, Sui Tang
In this paper, we focus on the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and body type. This model takes the form of a high-dimensional system of ordinary differential equations parameterized by two interaction kernels that appraise the alignment
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A kernel framework for learning differential equations and their solution operators Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-15 Da Long, Nicole Mrvaljević, Shandian Zhe, Bamdad Hosseini
This article presents a three-step kernel framework for regression of the functional form of differential equations (DEs) and learning their solution operators. Given a training set consisting of pairs of noisy DE solutions and source/boundary terms on a mesh: (i) kernel smoothing is utilized to denoise the data and approximate derivatives of the solution; (ii) This information is then used in a kernel
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Unsteady solute transport in Casson fluid flow and its retention in an atherosclerotic wall Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-14 Prosanjit Das, Sarifuddin, Mainul Haque, Prashanta Kumar Mandal
In the current study, a mathematical model of convective solute transport and its retention in an atherosclerotic wall is examined. The artery wall is supposed to be permeable and has cosine-shaped stenosis caused by various sorts of abnormal growth or plaque formation. The flowing blood is modeled as the suspension of all red blood cells in plasma, thought to be Casson fluid. The Immersed Boundary
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Learning dynamical systems from data: A simple cross-validation perspective, Part V: Sparse Kernel Flows for 132 chaotic dynamical systems Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-13 Lu Yang, Xiuwen Sun, Boumediene Hamzi, Houman Owhadi, Naiming Xie
Learning equations of complex dynamical systems from data is one of the principal problems in scientific machine learning. The method of Kernel Flows (KFs) has offered an effective learning strategy that interpolates the vector-field of dynamical system with a data-adapted kernel. It is based on the premise that a kernel is good if the number of interpolation points can be halved without significant
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Fractional-order effect on soliton wave conversion and stability for the two-Lévy-index fractional nonlinear Schrödinger equation with PT-symmetric potential Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-08 Fajun Yu, Li Li, Jiefang Zhang, Jingwen Yan
We investigate a variable-coefficient fractional nonlinear Schrödinger(vc-FNLS) equation with Wadati potential and PT-symmetric potential. We find the Lévy index can be used to transition from a breather wave to a soliton as the fractional order derivative is increasing. The influences of fractional and on the breather, dark and bright solitons of space–time vc-FNLS equation are analyzed in detail
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Runs of extremes of observables on dynamical systems and applications Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-08 Meagan Carney, Mark Holland, Matthew Nicol, Phuong Tran
We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fréchet (fat-tailed) or Weibull (bounded) distribution. The motivation for this work was to give estimates of the probabilities of sustained periods of weather anomalies such as heat-waves
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Bifurcations phenomena and route to chaos via the cosymmetry breaking in the Darcy convection problem Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-08 V, a, s, i, l, y, , N, ., , G, o, v, o, r, u, k, h, i, n
The purpose of this paper is to examine and exhibit bifurcations arising from cosymmetry breaking in dynamical systems. Curves of equilibria are typical of cosymmetric dynamical systems. Perturbations violating cosymmetry destroy these curves, leading to different attractors. An example of a cosymmetric problem is the Darcy convection in a rectangular vessel with a linear temperature profile on its
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A ternary phase-field model for two-phase flows in complex geometries Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-07 Chengjie Zhan, Zhenhua Chai, Baochang Shi
In this work, a ternary phase-field model for two-phase flows in complex geometries is proposed. In this model, one of the three components in the classical ternary Cahn–Hilliard model is considered as the solid phase, and only one Cahn–Hilliard equation with degenerate mobility needs to be solved due to the condition of volume conservation, which is consistent with the standard phase-field model with
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Equilibrium investment–reinsurance strategy under information asymmetry and random horizon Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-06 Wenhu Wang, Yankai Wang, Xingchun Peng
This paper investigates an investment–reinsurance problem incorporating information asymmetry and random horizon. At the beginning of the transaction, the insurer owns some inside information related to the risky asset price and the insurance claims. Simultaneously, the return rate and the driving noise for the risky asset process cannot be observed directly. Moreover, the trading horizon is random
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Synchronization of scale-free neuronal network with small-world property induced by spike-timing-dependent plasticity under time delay Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-06 Xueyan Hu, Yong Wu, Qianming Ding, Ying Xie, Zhiqiu Ye, Ya Jia
Spike-timing-dependent plasticity (STDP) is one of the important rules for the change of synaptic weights between neurons in biological nervous systems. In this paper, we study the effect of STDP on the synchronization phenomenon induced by time delay in the neuronal network which is the scale-free network with small-world property, and nodes of the network are constructed by Izhikevich neuron and
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Subharmonic Melnikov functions and nonintegrability for autonomous and non-autonomous perturbations of single-degree-of-freedom Hamiltonian systems near periodic orbits Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-06 S, h, o, y, a, , M, o, t, o, n, a, g, a
We study autonomous and non-autonomous perturbations of single-degree-of-freedom Hamiltonian systems and give sufficient conditions for their real-analytic non-integrability near periodic orbits of the unperturbed systems such that the first integrals and commutative vector fields depend analytically on the small parameter by using the subharmonic Melnikov functions. Moreover, we show that autonomous
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Unconditionally optimal time two-mesh mixed finite element algorithm for a nonlinear fourth-order distributed-order time fractional diffusion equation Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-06 Cao Wen, Jinfeng Wang, Yang Liu, Hong Li, Zhichao Fang
In this article, a fast second-order time two-mesh mixed finite element (TT-MMFE) algorithm is considered to numerically solve the nonlinear fourth-order distributed-order time fractional diffusion equation, where the generated formula for the fractional BDF2 and fractional trapezoidal rule through a free parameter (FBT- formula) combined with the composite trapezoid formula for the distributed-order
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The Entropy Economy and the Kolmogorov Learning Cycle: Leveraging the Intersection of Machine Learning and Algorithmic Information Theory to Jointly Optimize Energy and Learning Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-05 Scott C. Evans, Tapan Shah, Hao Huang, Sachini Piyoni Ekanayake
We augment the with energy cost and drive the concept of “Additive AI” where Machine Learning Models are created by traversing the Kolmogorov Structure function from low model complexity to high while seeking the Kolmogorov Minimum Sufficient Statistic with least energy cost. In this way, the intersection of Algorithmic Information Theory (AIT) with Machine Learning (ML) can enable optimization of
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Point-symmetry pseudogroup, Lie reductions and exact solutions of Boiti–Leon–Pempinelli system Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-05 Diana S. Maltseva, Roman O. Popovych
We carry out extended symmetry analysis of the (1+2)-dimensional Boiti–Leon–Pempinelli system, which corrects, enhances and generalizes many results existing in the literature. The point-symmetry pseudogroup of this system is computed using an original megaideal-based version of the algebraic method. A number of meticulously selected differential constraints allow us to construct families of exact
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Quasiclassical integrability condition in AKNS scheme Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-03 A.M. Kamchatnov, D.V. Shaykin
In this paper, we study the condition of quasiclassical integrability of soliton equations. This condition states that the Hamiltonian structure of equations, which govern propagation of high-frequency wave packets, is preserved by the dispersionless flow independently of initial data. If this condition is fulfilled, then the carrier wave number of any packet is a certain function of the local values
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A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller–Segel chemotaxis systems Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-03 Zhongjian Wang, Jack Xin, Zhiwen Zhang
We study a regularized interacting particle method for computing aggregation patterns and near singular solutions of a Keller–Segel (KS) chemotaxis system in two and three space dimensions, then further develop the DeepParticle method to learn and generate solutions under variations of physical parameters. The KS solutions are approximated as empirical measures of particles that self-adapt to the high
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Launching drifter observations in the presence of uncertainty Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-03 Nan Chen, Evelyn Lunasin, Stephen Wiggins
Determining the optimal locations for placing extra observational measurements has practical significance. However, the exact underlying flow field is never known in practice. Significant uncertainty appears when the flow field is inferred from a limited number of existing observations via data assimilation or statistical forecast. In this paper, a new computationally efficient strategy for deploying
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Impacts of diapause eggs on mosquito population suppression based on incompatible or sterile insect technique Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-03 Zian Wei, Xiaoyan Luo, Linchao Hu
Mosquito-borne diseases kill more than 700, 000 people a year, and the toll continues to rise. Controlling mosquito population is the key measure to prevent mosquito-borne diseases. Releasing sterile male mosquitoes to suppress wild mosquito population is an environmentally friendly and efficient method, which has been proven to successfully eliminate wild mosquitoes in laboratory, but it is difficult
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Adaptive loss weighting auxiliary output fPINNs for solving fractional partial integro-differential equations Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-02 Jingna Zhang, Yue Zhao, Yifa Tang
We propose an adaptive loss weighting auxiliary output fractional physics-informed neural networks (AWAO-fPINNs) based on the fractional physics-informed neural networks (fPINNs) for solving fractional partial integro-differential equations. In this framework, the automatic differentiation technique and numerical differentiation algorithm are effectively combined to construct a universal numerical
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Quasi-periodic breathers and rogue waves to the focusing Davey–Stewartson equation Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-02 Jianqing Sun, Xingbiao Hu, Yingnan Zhang
The Davey–Stewartson equation has been instrumental in describing various physical phenomena, especially (2+1)-dimensional breathers and rogue waves. In this paper, we present a direct approach to studying the quasi-periodic breathers of the Davey–Stewartson equation. By employing Hirota’s bilinear method and leveraging certain identities of theta functions, the problem is transformed into an over-determined
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Bifurcation analysis of a conceptual model for vertical mixing in the North Atlantic Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-01 John Bailie, Bernd Krauskopf
The Atlantic Meridional Overturning Circulation (AMOC) distributes heat and salt into the Northern Hemisphere via a warm surface current towards the subpolar North Atlantic, where water sinks and returns southwards as a deep cold current. There is substantial evidence that the AMOC has slowed down over the last century. We introduce a conceptual box model for the evolution of salinity and temperature
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Fast–slow analysis of passive mitigation of self-sustained oscillations by means of a bistable nonlinear energy sink Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-01 Baptiste Bergeot, Sébastien Berger
This paper investigates the dynamic behavior of a Van der Pol oscillator (used as an archetypal self-sustained oscillator) coupled to a bistable nonlinear energy sink (BNES). We first show using numerical simulations that this system can undergo a multitude of motions including different types of periodic regimes and so-called strongly modulated responses (SMR) as well as chaotic regimes. We also show
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Synchronization of uncertain chaotic systems with minimal parametric information Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-02-01 Syed Shadab Nayyer, Revati Gunjal, S.R. Wagh, N.M. Singh
The chaotic synchronization is mainly hampered by uncertain system dynamics in terms of underlying parameters. To obtain accurate parameter estimates for the proper synchronization of uncertain chaotic systems (UCSs) through adaptive control, it is necessary to satisfy the persistence of excitation (PE) condition. Furthermore, the challenges imposed by the explosion of complexity in sequential stabilization
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Linear instability and weakly nonlinear effects in eastward dipoles Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-30 J. Davies, I. Shevchenko, P. Berloff, G.G. Sutyrin
The linear instability and weakly nonlinear dynamics of eastward-propagating, steady-state Larichev–Reznik vortex dipoles are explored in terms of two-dimensional normal-mode analysis. To extract the fastest growing normal modes, we apply both breeding methodology based on solving the initial-value problem, as well as a direct-solution approach through the full-spectrum eigenproblem involving large
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On the non-integrable discrete focusing Hirota equation: Spatial properties, discrete solitons and stability analysis Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-29 Liyuan Ma, Haifang Song, Qiuyue Jiang, Shoufeng Shen
This paper focuses on various properties of the non-integrable discrete focusing Hirota (Hirota) equation, encompassing spatial structure, discrete solitons, and linear stability analysis. Through a planar nonlinear discrete dynamical map method, we construct the spatially periodic solutions of the non-integrable discrete stationary Hirota equation under special conditions. From the area-preserving
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Action–angle variables and conservation laws expressed in terms of scattering data for an integrable hierarchy associated with the Zakharov–Ito system Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-29 Zhi-Jia Wu, Shou-Fu Tian, Zhe-Yong Yin
In this work, the Poisson brackets for the scattering data of an integrable hierarchy for the Zakharov–Ito system are computed by employ the inverse scattering approach. Then, the action–angle variables and infinite conservation laws are expressed in terms of the scattering data. It is worth noting that, compared to previous works on Camassa–Holm equation and KdV-type equations, we have made some further
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Revisiting the Toda–Brumer–Duff criterion for order-chaos transition in dynamical systems Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-25 F. Sattin, L. Salasnich
The Toda–Brumer–Duff (TBD) is an analytical criterion for estimating the local exponential rate of divergence between nearby trajectories in dynamical systems, and it is employed as a test for assessing the existence of chaos therein. It is fairly simple, intuitive, and works well in several situations, hence gained quite a wide popularity, yet it is known to be not rigorous since predicts “false positives”
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Nonlinear stability of shock-fronted travelling waves in reaction-nonlinear diffusion equations Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-24 Ian Lizarraga, Robert Marangell
Reaction-nonlinear diffusion PDEs can be derived as continuum limits of stochastic models for biological and ecological invasion. We numerically investigate the nonlinear stability of shock-fronted travelling waves arising in these RND PDEs, in the presence of a fourth-order spatial derivative multiplied by a small parameter that models . Once we have verified sectoriality of our linear operator, our
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Long-timescale soliton dynamics in the Korteweg–de Vries equation with multiplicative translation-invariant noise Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-24 R.W.S. Westdorp, H.J. Hupkes
This paper studies the behavior of solitons in the Korteweg–de Vries equation under the influence of multiplicative noise. We introduce stochastic processes that track the amplitude and position of solitons based on a rescaled frame formulation and stability properties of the soliton family. We furthermore construct tractable approximations to the stochastic soliton amplitude and position which reveal
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On the collision dynamics in a molecular model Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-19 Esther Barrabés, Mercè Ollé, Óscar Rodríguez
We study the problem of the hydrogen atom submitted to a circularly polarized microwave field. This problem, analyzed from a classical mechanics approach, can be modeled by an autonomous Hamiltonian depending on one parameter . The paper is focused on the so called -ejection–collision orbits (-EC orbits), that is orbits that the electron describes when it ejects from the nucleus and collides with it
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On the Kadomtsev–Petviashvili equation with double-power nonlinearities Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-19 Amin Esfahani, Steven Levandosky, Gulcin M. Muslu
In this paper, we study the generalized KP equation with double-power nonlinearities. Our investigation covers various aspects, including the existence of solitary waves, their nonlinear stability, and instability. Notably, we address a broader class of nonlinearities represented by , with , encompassing cases where and . One of the distinct features of our work is the absence of scaling, which introduces
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Numerical simulation methods and analysis for the dynamics of the time-fractional KdV equation Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-19 Haiyan Cao, Xiujun Cheng, Qifeng Zhang
In this paper, two classes of efficient difference schemes for the simulation of the time-fractional Korteweg–de Vries equation are carried out. The temporal derivative is approximated with the help of the uniform/nonuniform formula and the uniform - formula, respectively. The spatial derivative is done with the uniform centered difference scheme. Unique solvability, boundedness and convergence of
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Stability and dynamics of regular and embedded solitons of a perturbed Fifth-order KdV equation Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-18 S. Roy Choudhury, Gaetana Gambino, Ranses Alfonso Rodriguez
Families of symmetric embedded solitary waves of a perturbed Fifth-order Korteweg–de Vries (FKdV) system were treated in Choudhury et al. (2022) using perturbative and reversible systems techniques. Here, the stability of those solutions, which was not considered in the earlier paper, is detailed. In addition, the results of Choudhury et al. (2022) are extended to the case of asymmetric solitary waves
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Applied and computational complex analysis in the study of nonlinear phenomena Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-18 Bartosz Protas, Stefan G. Llewellyn Smith, Takashi Sakajo
The theme issue surveys recent advances at the intersection between Applied and Computational Complex Analysis (ACCA) and the study of different nonlinear phenomena. While complex analysis has traditionally played an important role in the development of certain areas of physics, such as fluid and solid mechanics, in recent years there has been a resurgence of interest in new applications of complex
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Taming vibrational resonance by transient high frequency Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-17 M, ., , P, a, u, l, , A, s, i, r
We investigate the phenomenon of vibrational resonance (VR) in a model of two-fluid plasma driven by biharmonic forcing. We introduce a transient high-frequency (HF) signal by implementing the control parameter that clips the HF in rationale with the time period of the system. We found that one can efficiently tame the emergence and characteristics of VR with the introduction of . We study a coupled
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Effective reduced models from delay differential equations: Bifurcations, tipping solution paths, and ENSO variability Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-17 Mickaël D. Chekroun, Honghu Liu
Conceptual delay models have played a key role in the analysis and understanding of El Niño-Southern Oscillation (ENSO) variability. Based on such delay models, we propose in this work a novel scenario for the fabric of ENSO variability resulting from the subtle interplay between stochastic disturbances and nonlinear invariant sets emerging from bifurcations of the unperturbed dynamics.
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Edge of chaos as critical local symmetry breaking in dissipative nonautonomous systems Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-16 R, i, c, a, r, d, o, , C, h, a, c, ó, n
The fully nonlinear notion of resonancein the general context of dissipative systems subjected to spatially periodic potentials is discussed. It is demonstrated that there is an exact local invariant associated with each geometrical resonance solution which reduces to the system’s energy when the potential is stationary. The geometrical resonance solutions represent a whose critical breaking leads
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Coagulation, non-associative algebras and binary trees Phys. D Nonlinear Phenom. (IF 4.0) Pub Date : 2024-01-15 S, i, m, o, n, , J, ., A, ., , M, a, l, h, a, m
We consider the classical Smoluchowski coagulation equation with a general frequency kernel. We show that there exists a natural deterministic solution expansion in the non-associative algebra generated by the convolution product of the coalescence term. The non-associative solution expansion is equivalently represented by binary trees. We demonstrate that the existence of such solutions corresponds