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Nonlinear Network Dynamics with Consensus–Dissensus Bifurcation J. Nonlinear Sci. (IF 2.104) Pub Date : 2021-01-15 Karel Devriendt, Renaud Lambiotte
We study a nonlinear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and the dominating behaviour of a general class of nonlinear dynamical systems. The equilibrium behaviour of the system exhibits a global bifurcation with respect to the
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Transformation Cloaking in Elastic Plates J. Nonlinear Sci. (IF 2.104) Pub Date : 2021-01-13 Ashkan Golgoon, Arash Yavari
In this paper, we formulate the problem of elastodynamic transformation cloaking for Kirchoff–Love plates and elastic plates with both in-plane and out-of-plane displacements. A cloaking transformation maps the boundary-value problem of an isotropic and homogeneous elastic plate (virtual problem) to that of an anisotropic and inhomogeneous elastic plate with a hole surrounded by a cloak that is to
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Optimal Decay Estimates for 2D Boussinesq Equations with Partial Dissipation J. Nonlinear Sci. (IF 2.104) Pub Date : 2021-01-08 Suhua Lai, Jiahong Wu, Xiaojing Xu, Jianwen Zhang, Yueyuan Zhong
Buoyancy-driven fluids such as many atmospheric and oceanic flows and the Rayleigh–Bénard convection are modeled by the Boussinesq systems. By rigorously estimating the large-time behavior of solutions to a special Boussinesq system, this paper reveals a fascinating phenomenon on buoyancy-driven fluids that the temperature can actually stabilize the fluids. The Boussinesq system concerned here governs
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Stochastic SIR Lévy Jump Model with Heavy-Tailed Increments J. Nonlinear Sci. (IF 2.104) Pub Date : 2021-01-07 Nicolas Privault, Liang Wang
This paper considers a general stochastic SIR epidemic model driven by a multidimensional Lévy jump process with heavy-tailed increments and possible correlation between noise components. In this framework, we derive new sufficient conditions for disease extinction and persistence in the mean. Our method differs from previous approaches by the use of Kunita’s inequality instead of the Burkholder–Davis–Gundy
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Distributed Branch Points and the Shape of Elastic Surfaces with Constant Negative Curvature J. Nonlinear Sci. (IF 2.104) Pub Date : 2021-01-07 Toby L. Shearman, Shankar C. Venkataramani
We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic sheets, they carry a topological index which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating
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On Qualitative Behaviour of Solutions to a Thin Film Equation with a Source Term J. Nonlinear Sci. (IF 2.104) Pub Date : 2021-01-07 M. Chugunova, Y. Ruan, R. Taranets
In this article, we study a one-dimensional degenerate fourth-order parabolic equation (a thin-film model) with a source term. We prove existence of generalized weak solutions for the case \(n>0\) and study interface propagation properties like: finite speed propagation and waiting time phenomenon for the case \(1
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Convex Computation of Extremal Invariant Measures of Nonlinear Dynamical Systems and Markov Processes J. Nonlinear Sci. (IF 2.104) Pub Date : 2021-01-07 Milan Korda, Didier Henrion, Igor Mezić
We propose a convex-optimization-based framework for computation of invariant measures of polynomial dynamical systems and Markov processes, in discrete and continuous time. The set of all invariant measures is characterized as the feasible set of an infinite-dimensional linear program (LP). The objective functional of this LP is then used to single out a specific measure (or a class of measures) extremal
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Traveling Wave Solutions for a Class of Discrete Diffusive SIR Epidemic Model J. Nonlinear Sci. (IF 2.104) Pub Date : 2021-01-07 Ran Zhang, Jinliang Wang, Shengqiang Liu
This paper is concerned with the conditions of existence and nonexistence of traveling wave solutions (TWS) for a class of discrete diffusive epidemic model. We find that the existence of TWS is determined by the so-called basic reproduction number and the critical wave speed: When the basic reproduction number \(\mathfrak {R}_0>1\), there exists a critical wave speed \(c^*>0\), such that for each
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Effect of Discrete Breathers on the Specific Heat of a Nonlinear Chain J. Nonlinear Sci. (IF 2.104) Pub Date : 2021-01-07 Mohit Singh, Alina Y. Morkina, Elena A. Korznikova, Volodymyr I. Dubinko, Dmitry A. Terentiev, Daxing Xiong, Oleg B. Naimark, Vakhid A. Gani, Sergey V. Dmitriev
A nonlinear chain with sixth-order polynomial on-site potential is used to analyze the evolution of the total-to-kinetic-energy ratio during development of modulational instability of extended nonlinear vibrational modes. For the on-site potential of hard-type (soft-type) anharmonicity, the instability of \(q =\pi \) mode (\(q = 0\) mode) results in the appearance of long-living discrete breathers
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Classification of $$(n+1, 1)$$ ( n + 1 , 1 ) -Stacked Central Configurations in $$R^3$$ R 3 J. Nonlinear Sci. (IF 2.104) Pub Date : 2021-01-07 Xiang Yu, Shuqiang Zhu
We classify the extensions of n-body central configurations to \((n+1)\)-body central configurations in \(R^3\), in both the collinear case and the non-collinear case. We completely solve the two open questions posed by Hampton (Nonlinearity 18: 2299-2304, 2005). This classification is related with study on co-circular and co-spherical central configurations. We also obtain a general property of co-circular
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Scaling Limits for the Generalized Langevin Equation J. Nonlinear Sci. (IF 2.104) Pub Date : 2021-01-02 G. A. Pavliotis, G. Stoltz, U. Vaes
In this paper, we study the diffusive limit of solutions to the generalized Langevin equation (GLE) in a periodic potential. Under the assumption of quasi-Markovianity, we obtain sharp longtime equilibration estimates for the GLE using techniques from the theory of hypocoercivity. We then show asymptotic results for the effective diffusion coefficient in the small correlation time regime, as well as
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Nonlinear Theory for Coalescing Characteristics in Multiphase Whitham Modulation Theory J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-12-29 Thomas J. Bridges, Daniel J. Ratliff
The multiphase Whitham modulation equations with N phases have 2N characteristics which may be of hyperbolic or elliptic type. In this paper, a nonlinear theory is developed for coalescence, where two characteristics change from hyperbolic to elliptic via collision. Firstly, a linear theory develops the structure of colliding characteristics involving the topological sign of characteristics and multiple
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Dynamics of Shadow System of a Singular Gierer–Meinhardt System on an Evolving Domain J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-12-18 Nikos I. Kavallaris, Raquel Barreira, Anotida Madzvamuse
The main purpose of the current paper is to contribute towards the comprehension of the dynamics of the shadow system of a singular Gierer–Meinhardt model on an isotropically evolving domain. In the case where the inhibitor’s response to the activator’s growth is rather weak, then the shadow system of the Gierer–Meinhardt model is reduced to a single though non-local equation whose dynamics is thoroughly
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Stochastic Variational Formulations of Fluid Wave–Current Interaction J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-12-18 Darryl D. Holm
We are modelling multiscale, multi-physics uncertainty in wave–current interaction (WCI). To model uncertainty in WCI, we introduce stochasticity into the wave dynamics of two classic models of WCI, namely the generalised Lagrangian mean (GLM) model and the Craik–Leibovich (CL) model. The key idea for the GLM approach is the separation of the Lagrangian (fluid) and Eulerian (wave) degrees of freedom
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Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-12-18 Andreas Bittracher, Stefan Klus, Boumediene Hamzi, Péter Koltai, Christof Schütte
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parameterization of a low-dimensional transition manifold in a certain
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The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-12-18 Hui Huang, Jinniao Qiu
In this paper, we propose and study a stochastic aggregation–diffusion equation of the Keller–Segel (KS) type for modeling the chemotaxis in dimensions \(d=2,3\). Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence
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Lattice Solutions in a Ginzburg–Landau Model for a Chiral Magnet J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-09-25 Xinye Li, Christof Melcher
We examine micromagnetic pattern formation in chiral magnets, driven by the competition of Heisenberg exchange, Dzyaloshinskii–Moriya interaction, easy-plane anisotropy and thermodynamic Landau potentials. Based on equivariant bifurcation theory, we prove existence of lattice solutions branching off the zero magnetization state and investigate their stability. We observe in particular the stabilization
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A New Evans Function for Quasi-Periodic Solutions of the Linearised Sine-Gordon Equation J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-09-24 W. A. Clarke, R. Marangell
We construct a new Evans function for quasi-periodic solutions to the linearisation of the sine-Gordon equation about a periodic travelling wave. This Evans function is written in terms of fundamental solutions to a Hill’s equation. Applying the Evans-Krein function theory of Kollár and Miller (SIAM Rev 56(1):73–123, 2014) to our Evans function, we provide a new method for computing the Krein signatures
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Bounds on the Energy of a Soft Cubic Ferromagnet with Large Magnetostriction J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-09-19 Raghavendra Venkatraman, Vivekanand Dabade, Richard D. James
We complete the analysis initiated in Dabade et al. (J Nonlinear Sci 21:415–460, 2018) on the micromagnetics of cubic ferromagnets in which the role of magnetostriction is significant. We prove ansatz-free lower bounds for the scaling of the total micromagnetic energy including magnetostriction contribution, for a two-dimensional sample. This corresponds to the micromagnetic energy per unit length
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Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-09-10 Luzie Helfmann, Enric Ribera Borrell, Christof Schütte, Péter Koltai
Given two distinct subsets A, B in the state space of some dynamical system, transition path theory (TPT) was successfully used to describe the statistical behavior of transitions from A to B in the ergodic limit of the stationary system. We derive generalizations of TPT that remove the requirements of stationarity and of the ergodic limit and provide this powerful tool for the analysis of other dynamical
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Inflection, Canards and Folded Singularities in Excitable Systems: Application to a 3D FitzHugh–Nagumo Model J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-09-07 J. Uria Albizuri, M. Desroches, M. Krupa, S. Rodrigues
Specific kinds of physical and biological systems exhibit complex Mixed-Mode Oscillations mediated by folded-singularity canards in the context of slow-fast models. The present manuscript revisits these systems, specifically by analysing the dynamics near a folded singularity from the viewpoint of inflection sets of the flow. Originally, the inflection set method was developed for planar systems [Brøns
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Locality of Interatomic Interactions in Self-Consistent Tight Binding Models J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-09-04 Jack Thomas
A key starting assumption in many classical interatomic potential models for materials is a site energy decomposition of the potential energy surface into contributions that only depend on a small neighbourhood. Under a natural stability condition, we construct such a spatial decomposition for self-consistent tight binding models, extending recent results for linear tight binding models to the nonlinear
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Anomalous Waves Triggered by Abrupt Depth Changes: Laboratory Experiments and Truncated Kdv Statistical Mechanics J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-09-03 Nicholas J. Moore, C. Tyler Bolles, Andrew J. Majda, Di Qi
Recent laboratory experiments of Bolles et al. (Phys Rev Fluids 4(1):011801, 2019) demonstrate that an abrupt change in bottom topography can trigger anomalous statistics in randomized surface waves. Motivated by these observations, Majda et al. (Proc Natl Acad Sci 116(10):3982–3987, 2019) developed a theoretical framework, based on deterministic and statistical analysis of the truncated Korteweg-de
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The Rotating Rigid Body Model Based on a Non-twisting Frame J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-08-05 Cristian Guillermo Gebhardt, Ignacio Romero
This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all times and, thus, is represented by a nonholonomic restriction. Then, the corresponding Lagrange–D’Alembert equations are formulated by employing two descriptions
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Slow Unfoldings of Contact Singularities in Singularly Perturbed Systems Beyond the Standard Form J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-08-04 Ian Lizarraga, Robert Marangell, Martin Wechselberger
We develop the contact singularity theory for singularly perturbed (or ‘slow–fast’) vector fields of the general form \(z' = H(z,\varepsilon )\), \(z\in {\mathbb {R}}^n\) and \(0 < \varepsilon \ll 1\). Our main result is the derivation of computable, coordinate-independent defining equations for contact singularities under an assumption that the leading-order term of the vector field admits a suitable
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Propagation Speed of the Bistable Traveling Wave to the Lotka–Volterra Competition System in a Periodic Habitat J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-07-22 Hongyong Wang, Chunhua Ou
We study propagation direction of the traveling wave for the diffusive Lotka–Volterra competition system with bistable nonlinearity in a periodic habitat. By directly proving the strong stability of two semitrivial equilibria, we establish a new and sharper result on the existence of traveling wave. Using the method of upper and lower solutions, we provide two comparison theorems concerning the direction
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The Quasiconvex Envelope of Conformally Invariant Planar Energy Functions in Isotropic Hyperelasticity J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-07-21 Robert J. Martin, Jendrik Voss, Ionel-Dumitrel Ghiba, Oliver Sander, Patrizio Neff
We consider conformally invariant energies W on the group \({{\,\mathrm{GL}\,}}^{\!+}(2)\) of \(2\times 2\)-matrices with positive determinant, i.e., \(W:{{\,\mathrm{GL}\,}}^{\!+}(2)\rightarrow {\mathbb {R}}\) such that $$\begin{aligned} W(A\, F\, B) = W(F) \quad \text {for all }\; A,B\in \{a\, R\in {{\,\mathrm{GL}\,}}^{\!+}(2) \,|\,a\in (0,\infty ),\; R\in {{\,\mathrm{SO}\,}}(2)\}, \end{aligned}$$
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The Derivative Nonlinear Schrödinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms and N -Double-Pole Solutions J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-07-17 Guoqiang Zhang, Zhenya Yan
In this paper, we report a rigorous theory of the inverse scattering transforms (ISTs) for the derivative nonlinear Schrödinger (DNLS) equation with both zero boundary conditions (ZBCs) and nonzero boundary conditions (NZBCs) at infinity and double zeros of analytical scattering coefficients. The scattering theories for both ZBCs and NZBCs are addressed. The direct scattering problem establishes the
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Hill Four-Body Problem with Oblate Bodies: An Application to the Sun–Jupiter–Hektor–Skamandrios System J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-07-16 Jaime Burgos-García, Alessandra Celletti, Catalin Gales, Marian Gidea, Wai-Ting Lam
We consider a restricted four-body problem, with a precise hierarchy between the bodies: two larger bodies and a smaller one, all three of oblate shape, and a fourth, infinitesimal body, in the neighborhood of the smaller of the three bodies. The three heavy bodies are assumed to move in a plane under their mutual gravity, and the fourth body to move in the three-dimensional space under the gravitational
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Rogue Waves in the Generalized Derivative Nonlinear Schrödinger Equations J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-07-15 Bo Yang, Junchao Chen, Jianke Yang
General rogue waves are derived for the generalized derivative nonlinear Schrödinger (GDNLS) equations by a bilinear Kadomtsev–Petviashvili (KP) reduction method. These GDNLS equations contain the Kaup–Newell equation, the Chen–Lee–Liu equation and the Gerdjikov–Ivanov equation as special cases. In this bilinear framework, it is shown that rogue waves to all members of these equations are expressed
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On the Geometric Diversity of Wavefronts for the Scalar Kolmogorov Ecological Equation J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-07-15 Karel Hasík, Jana Kopfová, Petra Nábělková, Sergei Trofimchuk
We answer three fundamental questions concerning monostable traveling fronts for the scalar Kolmogorov ecological equation with diffusion and spatiotemporal interaction: These are the questions about their existence, uniqueness and geometric shape. In the particular case of the food-limited model, we give a rigorous proof of the existence of a peculiar, yet substantive and nonlinearly determined class
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Turbulent Energy Spectrum via an Interaction Potential J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-07-14 Rafail V. Abramov
For a large system of identical particles interacting by means of a potential, we find that a strong large scale flow velocity can induce motions in the inertial range via the potential coupling. This forcing lies in special bundles in the Fourier space, which are formed by pairs of particles. These bundles are not present in the Boltzmann, Euler and Navier–Stokes equations, because they are destroyed
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Asymptotic Solution of a Boundary Value Problem for a Spring–Mass Model of Legged Locomotion J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-07-06 Hanna Okrasińska-Płociniczak, Łukasz Płociniczak
Running is the basic mode of fast locomotion for legged animals. One of the most successful mathematical descriptions of this gait is the so-called spring–mass model constructed upon an inverted elastic pendulum. In the description of the grounded phase of the step, an interesting boundary value problem arises where one has to determine the leg stiffness. In this paper, we find asymptotic expansions
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Nonlinear Physiologically Structured Population Models with Two Internal Variables J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-06-27 Hao Kang, Xi Huo, Shigui Ruan
First-order hyperbolic partial differential equations with two internal variables have been used to model biological and epidemiological problems with two physiological structures, such as chronological age and infection age in epidemic models, age and another physiological character (maturation, size, stage) in population models, and cell-age and molecular content (cyclin content, maturity level,
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Phase Separation in the Advective Cahn–Hilliard Equation J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-06-18 Yu Feng, Yuanyuan Feng, Gautam Iyer, Jean-Luc Thiffeault
The Cahn–Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn–Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing, then no phase separation occurs, and the solution instead
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Weak Solutions Obtained by the Vortex Method for the 2D Euler Equations are Lagrangian and Conserve the Energy J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-06-10 Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
We discuss the Lagrangian property and the conservation of the kinetic energy for solutions of the 2D incompressible Euler equations. Existence of Lagrangian solutions is known when the initial vorticity is in \(L^p\) with \(1\le p\le \infty \), and if \(p\ge 3/2\), all weak solutions are conservative. In this work, we prove that solutions obtained via the vortex method are Lagrangian, and that they
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Correction to: Asymptotic Formulas for Extreme Statistics of Escape Times in 1, 2 and 3-Dimensions J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-06-09 K. Basnayake, Z. Schuss, D. Holcman
In section 5.1 entitled “The shortest NEP from a bounded domain in prviously.
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On Fast–Slow Consensus Networks with a Dynamic Weight J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-06-05 Hildeberto Jardón-Kojakhmetov, Christian Kuehn
We study dynamic networks under an undirected consensus communication protocol and with one state-dependent weighted edge. We assume that the aforementioned dynamic edge can take values over the whole real numbers, and that its behaviour depends on the nodes it connects and on an extrinsic slow variable. We show that, under mild conditions on the weight, there exists a reduction such that the dynamics
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Phase Transitions and Macroscopic Limits in a BGK Model of Body-Attitude Coordination J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-05-30 P. Degond, A. Diez, A. Frouvelle, S. Merino-Aceituno
In this article we investigate the phase transition phenomena that occur in a model of self-organisation through body-attitude coordination. Here, the body attitude of an agent is modelled by a rotation matrix in \({\mathbb {R}}^3\) as in Degond et al. (Math Models Methods Appl Sci 27(6):1005–1049, 2017). The starting point of this study is a BGK equation modelling the evolution of the distribution
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Closed Unstretchable Knotless Ribbons and the Wunderlich Functional J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-05-22 Brian Seguin, Yi-chao Chen, Eliot Fried
In 1962, Wunderlich published the article “On a developable Möbius band,” in which he attempted to determine the equilibrium shape of a free standing Möbius band. In line with Sadowsky’s pioneering works on Möbius bands of infinitesimal width, Wunderlich used an energy minimization principle, which asserts that the equilibrium shape of the Möbius band has the lowest bending energy among all possible
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A Geometric Heat-Flow Theory of Lagrangian Coherent Structures J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-05-19 Daniel Karrasch; Johannes Keller
We consider Lagrangian coherent structures (LCSs) as the boundaries of material subsets whose advective evolution is metastable under weak diffusion. For their detection, we first transform the Eulerian advection–diffusion equation to Lagrangian coordinates, in which it takes the form of a time-dependent diffusion or heat equation. By this coordinate transformation, the reversible effects of advection
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On the Detuned $$2\!{:}\!4$$2:4 Resonance J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-05-18 Heinz Hanßmann, Antonella Marchesiello, Giuseppe Pucacco
We consider families of Hamiltonian systems in two degrees of freedom with an equilibrium in 1 : 2 resonance. Under detuning, this “Fermi resonance” typically leads to normal modes losing their stability through period-doubling bifurcations. For cubic potentials, this concerns the short axial orbits, and in galactic dynamics, the resulting stable periodic orbits are called “banana” orbits. Galactic
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Spike-Adding Canard Explosion in a Class of Square-Wave Bursters J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-05-14 Paul Carter
This paper examines a spike-adding bifurcation phenomenon whereby small-amplitude canard cycles transition into large-amplitude bursting oscillations along a single continuous branch in parameter space. We consider a class of three-dimensional singularly perturbed ODEs with two fast variables and one slow variable and singular perturbation parameter \(\varepsilon \ll 1 \) under general assumptions
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The Regularized Visible Fold Revisited J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-05-11 K. Uldall Kristiansen
The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter \(\epsilon \rightarrow 0\). Alternatively, these singularly perturbed systems can be thought of as regularizations of their piecewise counterparts. The main contribution of the paper
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Dynamical Analysis and Control Strategies of Rumor Spreading Models in Both Homogeneous and Heterogeneous Networks J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-05-04 Linhe Zhu, Mengtian Zhou, Zhengdi Zhang
In recent years, rumor propagation in social networks attracts more researchers’ attention. In this paper, we have established I2S2R rumor spreading models in both homogeneous networks and heterogeneous networks considering the effect of time delay. In the homogeneous network model, we obtain the basic reproduction number by means of the next-generation matrix. Besides, the local stability and the
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Mathematical Analysis of Two Competing Cancer Cell Migration Mechanisms Driven by Interstitial Fluid Flow J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-04-23 Steinar Evje; Michael Winkler
Recent experimental work has revealed that interstitial fluid flow can mobilize two types of tumor cell migration mechanisms. One is a chemotactic-driven mechanism where chemokine (chemical component) bounded to the extracellular matrix (ECM) is released and skewed in the flow direction. This leads to higher chemical concentrations downstream which the tumor cells can sense and migrate toward. The
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Correction to: Spatiotemporal Pattern Extraction by Spectral Analysis of Vector-Valued Observables J. Nonlinear Sci. (IF 2.104) Pub Date : 2019-10-22 Dimitrios Giannakis, Abbas Ourmazd, Joanna Slawinska, Zhizhen Zhao
The original version of this article unfortunately contained an error in Acknowledgement section. The authors would like to correct the error with this erratum. The correct text should read as:
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Perihelion Librations in the Secular Three-Body Problem J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-04-17 Gabriella Pinzari
A normal form theory for non-quasiperiodic systems is combined with the special properties of the partially averaged Newtonian potential pointed out in Pinzari (Celest Mech Dyn Astron 131(5):22, 2019) to prove, in the averaged, planar three-body problem, the existence of a plenty of motions where, periodically, the perihelion of the inner body affords librations about one equilibrium position and its
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On the Gamma Convergence of Functionals Defined Over Pairs of Measures and Energy-Measures J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-03-19 Marco Caroccia; Riccardo Cristoferi
A novel general framework for the study of \(\Gamma \)-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the \(\Gamma \)-limit of these kind of functionals by knowing the \( \Gamma \)-limit of the underlying energies. In particular, the interaction between the functionals and the underlying energies results, in the case these
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Global Smooth Solutions for 1D Barotropic Navier–Stokes Equations with a Large Class of Degenerate Viscosities J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-03-11 Moon-Jin Kang; Alexis F. Vasseur
We prove the global existence and uniqueness of smooth solutions to the one-dimensional barotropic Navier–Stokes system with degenerate viscosity \(\mu (\rho )=\rho ^\alpha \). We establish that the smooth solutions have possibly two different far-fields, and the initial density remains positive globally in time, for the initial data satisfying the same conditions. In addition, our result works for
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Selection of Quasi-stationary States in the Stochastically Forced Navier–Stokes Equation on the Torus J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-03-04 Margaret Beck; Eric Cooper; Gabriel Lord; Konstantinos Spiliopoulos
The stochastically forced vorticity equation associated with the two-dimensional incompressible Navier–Stokes equation on \(D_\delta :=[0,2\pi \delta ]\times [0,2\pi ]\) is considered for \(\delta \approx 1\), periodic boundary conditions, and viscosity \(0<\nu \ll 1\). An explicit family of quasi-stationary states of the deterministic vorticity equation is known to play an important role in the long-time
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On Data-Driven Computation of Information Transfer for Causal Inference in Discrete-Time Dynamical Systems J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-03-03 S. Sinha; U. Vaidya
In this paper, we provide a novel approach to capture causal interaction in a dynamical system from time series data. In Sinha and Vaidya (in: IEEE conference on decision and control, pp 7329–7334, 2016), we have shown that the existing measures of information transfer, namely directed information, Granger causality and transfer entropy, fail to capture the causal interaction in a dynamical system
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Integrability Analysis of the Stretch–Twist–Fold Flow J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-02-25 Andrzej J. Maciejewski; Maria Przybylska
We study the integrability of an eight-parameter family of three-dimensional spherically confined steady Stokes flows introduced by Bajer and Moffatt. This volume-preserving flow was constructed to model the stretch–twist–fold mechanism of the fast dynamo magnetohydrodynamical model. In particular we obtain a complete classification of cases when the system admits an additional Darboux polynomial of
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Particle Filters with Nudging in Multiscale Chaotic Systems: With Application to the Lorenz ’96 Atmospheric Model J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-02-18 Hoong C. Yeong; Ryne T. Beeson; N. Sri Namachchivaya; Nicolas Perkowski
This paper presents reduced-order nonlinear filtering schemes based on a theoretical framework that combines stochastic dimensional reduction and nonlinear filtering. Here, dimensional reduction is achieved for estimating the slow-scale process in a multiscale environment by constructing a filter using stochastic averaging results. The nonlinear filter is approximated numerically using the ensemble
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On a Predator–Prey System with Digestion Delay and Anti-predation Strategy J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-02-15 Yang Wang; Xingfu Zou
Predator–prey interactions are among the most complicated interactions between biological species, in which there may be both direct effect (through predation) and indirect effect (e.g., fear effect). In the literature, the indirect effect has been largely missing in predator–prey models, until some recent works. Based on the recent work (Wang et al. in J Math Biol 73:1179–1204, 2016) where a fear
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Dynamics of Nonconstant Steady States of the Sel’kov Model with Saturation Effect J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-02-12 Zengji Du; Xiaoni Zhang; Huaiping Zhu
In this paper, we deal with Sel’kov model with saturation law which has been applied to numerous problems in chemistry and biology. We will study the stability of the unique constant steady state, existence and nonexistence of nonconstant steady states of such models. In particular, we prove that Turing pattern may occur when the saturation coefficient is small but will not occur when the coefficient
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Implications of Kunita–Itô–Wentzell Formula for k -Forms in Stochastic Fluid Dynamics J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-02-11 Aythami Bethencourt de Léon; Darryl D. Holm; Erwin Luesink; So Takao
We extend the Itô–Wentzell formula for the evolution of a time-dependent stochastic field along a semimartingale to k-form-valued stochastic processes. The result is the Kunita–Itô–Wentzell (KIW) formula for k-forms. We also establish a correspondence between the KIW formula for k-forms derived here and a certain class of stochastic fluid dynamics models which preserve the geometric structure of deterministic
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On Liouville Type Theorem for Stationary Non-Newtonian Fluid Equations J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-02-08 Dongho Chae; Jörg Wolf
In this paper, we prove a Liouville type theorem for non-Newtonian fluid equations in \(\mathbb R^3\), having the diffusion term \({\varvec{A}}_p( u)=\nabla \cdot ( |{\varvec{D}}(u)|^{p-2} {\varvec{D}}(u))\) with \( {\varvec{D}}(u) = \frac{1}{2} (\nabla u + (\nabla u)^{ \top })\), \(3/2
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A Kac Model for Kinetic Annihilation J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-02-07 Bertrand Lods; Alessia Nota; Federica Pezzotti
In this paper, we consider the stochastic dynamics of a finite system of particles in a finite volume (Kac-like particle system) which annihilate with probability \(\alpha \in (0,1)\) or collide elastically with probability \(1-\alpha \). We first establish the well-posedness of the particle system which exhibits no conserved quantities. We rigorously prove that, in some mean-field limit, a suitable
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Amplitude and Frequency Variation in Nonlinear Glucose Dynamics with Multiple Delays via Periodic Perturbation J. Nonlinear Sci. (IF 2.104) Pub Date : 2020-02-03 Adam Bridgewater; Benoit Huard; Maia Angelova
Characterising the glycemic response to a glucose stimulus is an essential tool for detecting deficiencies in humans such as diabetes. In the presence of a constant glucose infusion in healthy individuals, it is known that this control leads to slow oscillations as a result of feedback mechanisms at the organ and tissue level. In this paper, we provide a novel quantitative description of the dependence
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