Defect formation and transport in a hydrogen-bonded system is studied via a two-sublattice soliton-bearing one-dimensional model. Our two component model completes and extends our previous study (Tchakoutio Nguetcho and Kofane, 2007; Tchakoutio Nguetcho et al., 2008; Li et al., 2015) made on the dynamics of defects in a quasi-one-dimensional nonlinear model of complex hydrogen bond systems. The inclusion

The five libration points of a sun–planet system are stable or unstable fixed positions at which satellites or asteroids can remain fixed relative to the two orbiting bodies. A moon orbiting around the planet causes a time-dependent perturbation on the system. Here, we address the sense in which invariant structure remains. We employ a transition state theory developed previously for periodically driven

We analyze a variable-order time-fractional wave equation, which models, e.g., the vibration of a membrane in a viscoelastic environment. We prove that the solutions to the variable-order ordinary differential equations in the spectral decomposition of the solution to the fractional wave equation exhibit power-law decaying characteristics and overcome the difficulty that its solution operator does

Previously, some of us put forward the Lévy sections theorem revisited as an extension of the classical central limit theorem that provides an alternative view of data volatilities (Figueiredo et al., 2007a, 2007b). In this paper, we discuss its usefulness in the risk assessment of financial assets. Although it is a stylized fact that prices are likely to follow non-Gaussian random walks, time randomization

Biases impair the effectiveness of algorithms. For example, the age bias of the widely-used PageRank algorithm impairs its ability to effectively rank nodes in growing networks. PageRank’s temporal bias cannot be fully explained by existing analytic results that predict a linear relation between the expected PageRank score and the indegree of a given node. We show that in evolving networks, under a

Conventional sliding-modes based differentiators make it possible to estimate successive derivatives of a given time-varying signal in finite-time and with exact convergence in noise free case. In general, the convergence time is an unbounded increasing function of initial estimation errors. Most already proposed solutions guarantee a convergence in a maximum time independent of initial conditions

In this paper we consider a hyperbolic-exponential model of growth with density regulation and two different stages, following the scheme proposed in Rodríguez (1998). We analyze the dynamics and the complexity of the system, in particular, we study the existence and stability of the fixed points in terms of the W Lambert function and the existence of chaos is proved for a range of parameter values

A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of dynamics, characteristic for central pattern generators: respectively, in-phase, anti-phase synchronous oscillations and quiescence, and study various bifurcation transitions

The distance correlation (DC) statistics is capable of describing the nonlinear correlation between random variables, which is the extension and reinforcement of the existing Pearson correlation coefficient, Spearman rank correlation coefficient, Kendall coefficient of concordance, etc. However, there are difficulties in using the DC statistics to measure the dynamical features of complex signals directly

In this paper we revisit the (2+1)-dimensional mixed AKNS hierarchy recently studied by Gürses and Pekcan (2019, 2021). We present a unified bilinear form for the whole hierarchy and solutions in double Wronskian form. Local and nonlocal reductions of the hierarchy are considered and explicit N-soliton solutions for the reduced equations are obtained by means of a reduction technique on double Wronskians

In this paper, we study optimal control problems on the internal energy for a system governed by a class of elliptic boundary hemivariational inequalities with a parameter. The system has been originated by a steady-state heat conduction problem with non-monotone multivalued subdifferential boundary condition on a portion of the boundary of the domain described by the Clarke generalized gradient of

In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear dynamics literature that this mathematical technique can provide valuable information and insights to develop a more general and detailed understanding of the global behavior

Classically, cellular automata and, in fact, automata networks in general, have synchronous dynamics defined by a local function. But the interest on asynchronous versions of both systems has grown, since it provides an extra degree of freedom. The standard way to define deterministic asynchronism is to set an update priority to each node. It has been shown that these networks can solve problems that

Fluid-conveying nanotubes are important components in nano-electromechanical systems requiring strict static and dynamic stiffness designs. The nonlinear bending and forced vibration of the fluid-conveying functionally graded nanotubes in pre- and post-buckling states are investigated. Based on Zhang–Fu’s refined displacement field, a comprehensive size-dependent nanotube model is established in which

We give the topological classification of the global phase portraits in the Poincaré disc of the Kolmogorov systems ẋ=xa0+c1x+c2z2+c3z,ż=zc0+c1x+c2z2+c3z,which depend on five parameters and have infinitely many singular points at the infinity. We prove that these systems have 22 topologically distinct phase portraits.

The basilar membrane (BM) is the key infrastructure that supports the microstructure of cochlear acoustic function, and its interaction with lymph in the cochlea involves a complex, highly nonlinear coupling motion and energy conversion. In 1928, Nobel Laureate Gordon von Békésy experimented and first discovered the traveling wave motion of the BM, thus uncovering the mystery of BM motion. However

In order to understand better the fractal structure attached to the bifurcation diagrams it is required to identify the fractal structures underlying that diagram. With that objective we will first construct the explicit form of the structure and morphology of MSS-sequences (shift-maximal) that appear in bifurcation diagrams of a wide class of unimodal maps. Next we will derive and prove the theorems

In this paper, it is shown how a nonlinear elastic mechanical system can be exploited to increase the elastic potential energy compared to its linear counterpart. A strategy for optimizing the system parameters is proposed, and performance is compared considering equal maximum displacement and maximum force. A theoretical insight is presented, and some asymptotic trends for optimum parameters selection

Modeling information diffusion in social networks is very important for predicting and controlling diffusions. Various types of diffusion models exist considering different properties of information diffusion. Recently it was shown that information diffusion in social networks like Digg and Twitter is anomalous, but it is not addressed in any information diffusion model. In this paper, a new mathematical

In the present paper, we focus on a class of multivalued variational–hemivariational inequalities with pseudomonotone operator and constraint set in Hilbert spaces. By employing the penalty method and the Moreau–Yosida approximation technique, we construct an approximating problem for the original multivalued variational–hemivariational inequality under consideration. The main result in the paper shows

Critical slowing down arises close to bifurcations and involves long transients. Despite slowing down phenomena have been widely studied in local bifurcations i.e., bifurcations of equilibrium points, less is known about transients delay phenomena close to global bifurcations. In this paper, we identify a novel mechanism of slowing down arising in the vicinity of a global bifurcation identified in

In soft elastic solids, directional shear waves are in general governed by coupled nonlinear KZK-type equations for the two transverse velocity components, when both quadratic nonlinearity and cubic nonlinearity are taken into account. Here we consider spatially two-dimensional wave fields. We propose a change of variables to transform the equations into a quasi-linear first-order system of partial

This paper deals with the asymptotic spreading for a class of diffusion equations with degenerate monostable nonlinearity, where the initial value is asymptotically front-like. By the method of squeezing technique and super- and sub-solutions, we prove that the speed of asymptotic spreading may be finite or infinite, which depends on the degeneracy of nonlinearity as well as the decaying rate of the

A new mixed variational–hemivariational problem is introduced, a(u,v−u)+b(v−u,λ)+φ(v)−φ(u)+J0(Tu;Tv−Tu)≥(f,v−u)X, b(u,μ−λ)−ψ(μ)+ψ(λ)−Ψ0(Rλ;Rμ−Rλ)≤0, (v∈X, μ∈Λ⊆Y), focusing on its well-posedness. We are looking for a pair solution (u,λ)∈X×Λ working into a Hilbert spaces framework. Some particular cases with applications in mechanics are highlighted. A special attention is payed to a particular case

This paper addresses the construction and the stability of self-similar solutions to the isentropic compressible Euler equations. These solutions model a gas that implodes isotropically, ending in a singularity formation in finite time. The existence of smooth solutions that vanish at infinity and do not have vacuum regions was recently proved and, in this paper, we provide the first construction of

In this paper, we present a systematic renormalization group method to investigate a class of singularly perturbed delay differential equations. The uniformly valid approximate solution can be obtained, and we give a rigorous proof of the error estimate of the approximate solution. In addition, some numerical comparisons between the exact solution, the result by the averaging method and our result

The topological underpinning of magnetic fields connected to a planar boundary is naturally described by field line winding. This observation leads to the definition of winding helicity, which is closely related to the more commonly calculated relative helicity. Winding helicity, however, has several advantages, and we explore some of these in this work. In particular, we show, by splitting the domain

We develop a new quantifier for forward time uncertainty for trajectories that are solutions of models generated from data sets. Our uncertainty quantifier is defined on the phase space in which the trajectories evolve and we show that it has a rich structure that is directly related to phase space structures from dynamical systems theory, such as hyperbolic trajectories and their stable and unstable

In this paper we consider a class of feedback control systems described by an evolution hemivariational inequality involving history-dependent operators. Under the mild conditions, first, we prove a priori estimates of the solutions to the feedback control system. Then, an existence theorem for the feedback control system is obtained by using the well-known Bohnenblust-Karlin fixed point theorem. Moreover

This paper presents a new semi-analytical approach, namely the enhanced time-domain minimum residual method to solve the semi-analytical quasi-periodic solution for nonlinear system. This approach does not require multiple numerical integration and can be applied to strongly nonlinear systems. The approach is mainly three-fold. Firstly, the semi-analytical solution of the nonlinear quasi-periodic system

Most of CD4+ T cells die from pyroptosis which is an intensely inflammatory form of programmed cell death mediated by caspase-1. Inflammation is a major factor in the initiation and drive of some diseases, such as tumors, infectious diseases and atherosclerotic diseases. Recently, a new chemical inhibitor (Necrosulfonamide) has been confirmed to play a crucial role in the inhibition of pyroptosis.

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the solutions to a class of problems. We demonstrate this idea by estimating the coercive field of permanent magnets which depends on the width and strength of local

In this work, one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) coupled damped Schrödinger system is solved numerically. A strong-form local meshless approach established on radial basis function-finite difference (RBF-FD) method for spatial approximation is developed. Polyharmonic splines are used as radial basis function with augmented polynomials. The use of the polyharmonic

In this paper, we further extend the theories of Lie symmetry group and conservation law to study the time-fractional b-family peakon equations. The main distinction of the equations with the usual time-fractional partial differential equations is the mixed derivative of Riemann-Liouville time-fractional derivative and integer-order x-derivative. Thus we first give a prolongation formula of the infinitesimal

Brain tumours are masses of abnormal cells that can grow in an uncontrolled way in the brain. There are different types of malignant brain tumours. Gliomas are malignant brain tumours that grow from glial cells and are identified as astrocytoma, oligodendroglioma, and ependymoma. We study a mathematical model that describes glia-neuron interaction, glioma, and chemotherapeutic agent. In this work,

Nonlinear lattices support delocalized nonlinear vibrational modes (DNVMs) that are exact solutions to the dynamical equations of motion dictated by the lattice symmetry. Since only lattice symmetry is taken into consideration for derivation of DNVMs, they exist regardless the type of interaction between lattice points, and for arbitrary large amplitude. Here, considering space symmetry group of the

A non-linear system of Volterra integro-fractional delay differential equations with Caputo fractional derivatives is considered. New sufficient conditions for uniform stability, asymptotic stability, and Mittag-Leffler stability of the zero solution of the unperturbed system, and the boundedness of all solutions of the perturbed system, are presented. The technique of proof involves the Razumikhin

Quantitative quadratic physical observables pertaining to the longitudinal and transverse scattering asymmetry parameters are described in the context of the acoustic scattering theory, and their generalized mathematical expressions are derived for a cylinder material submerged in a non-viscous fluid and located arbitrarily in the field of an acoustical sheet of arbitrary shape (or beam in 2D). The

The effect of the asymmetric parameter in the dynamics, both of the forced Duffing van der Pol (DVdP) system and of the forced generalized Bonhoeffer-van der Pol (BVdP) system is investigated, namely the possibility for these systems to execute dynamics chaos even for large values of this asymmetric parameter. We have shown that the dynamics of the associated non dissipative and unforced system can

We show that the theory of classical Hamiltonian systems admitting separating variables can be formulated in the context of (ω,H) structures. They are symplectic manifolds endowed with a compatible Haantjes algebra H, namely an algebra of (1,1) tensor fields with vanishing Haantjes torsion. A special class of coordinates, called Darboux-Haantjes coordinates, will be constructed from the Haantjes algebras

This work investigates intermodal targeted energy transfers (IMTET) for passive mitigation of a large-scale nine-story structure subjected to blast excitation. This is achieved by inducing extreme, fast time scale energy transfers from lower-frequency structural modes which are mainly excited by the blast to higher-frequency ones. These targeted (directed) energy transfers are governed by a non-resonant

We investigate the dynamics of charged dust interacting with the interplanetary magnetic field in a Parker spiral type model and subject to the solar wind and Poynting-Robertson effect in the vicinity of the 1:1 mean motion resonance with planet Jupiter. We estimate the shifts of the location of the minimum libration amplitude solutions close to the location of the L4 and L5 points of the classical

The present study is concerned with the dynamics of special localized solutions emerging in the mass-in-mass anharmonic oscillatory chain in the state of acoustic vacuum. Each outer element of the chain incorporates an additional, purely nonlinear mass attachment. Using the homogeneity of the system under consideration, we use the separation of time and space and reduce the analysis of standing wave

We present a numerical framework for estimating the effective reproduction number of infectious diseases from compartmental epidemic models. The idea is to augment the reproduction number as an extended state variable in the model. We assume the reproduction number is a piece-wise constant function with jumps every new data are recorded. The numerical framework is written in discrete-time and is combined

Thermoelastic damping is a major source of intrinsic damping in vacuum operated Micro Electro Mechanical Systems (MEMS). In this article, the non-linear vibration of electrically actuated curved micro-beams is investigated, considering the effect of thermoelastic damping. The coupled thermoelasticity equations are derived on the basis of non-classical formulation, which is the modified couple stress

In this paper, kink scattering in the dimensional reduction of the bosonic sector of a one-parameter family of generalized Wess-Zumino models with three vacuum points is discussed. The value of the model parameter determines the specific location of the vacua. The influence of the vacuum arrangements (evolving from three collinear vacua to three vacua placed at the vertices of an equilateral triangle)

Being a vital two-dimensional multibody interacting particle system in nonlinear science and complex systems, exclusion network fuses totally asymmetric simple exclusion process into underlying complex network dynamics. This study constructs equiprobable exclusion network with heterogeneous interactions by introducing randomly generated interaction rates on each random path. Nodes are equivalent to

This paper is devoted to the numerical solution of a fourth-order elliptic variational inequality of the first kind by the virtual element method (VEM). The variational inequality models an obstacle problem for the Kirchhoff-Love plate. Both conforming and fully nonconforming VEMs are studied to solve the fourth-order elliptic variational inequality. Optimal order error estimates are derived in the

Global optimisation problems in high-dimensional and infinite-dimensional spaces arise in various real-world applications such as engineering, economics and finance, geophysics, biology, machine learning, optimal control, etc. Among stochastic approaches to global optimisation, biology-inspired methods are currently very popular in the literature. Bio-inspired approaches imitate natural ecological

The Veselov approach provides a discrete formulation of the Euler–Lagrange equation. To get this, a discrete Lagrangian version of a continuous one is considered and then a variational process is used. This problem has been studied in many papers by different authors, according to references and therein citations. This type of discretization can be useful in the case when the continuous Euler–Lagrange

In this paper we demonstrate the capability of the method of Lagrangian descriptors to unveil the phase space structures that characterize transport in high-dimensional symplectic maps. In order to illustrate its use, we apply it to a four-dimensional symplectic map model that is used in chemistry to explore the nonlinear dynamics of van der Waals complexes. The advantage of this technique is that

The characteristic (Laplace or Lévy) exponents uniquely characterize infinitely divisible probability distributions. Although of purely mathematical origin they appear to be uniquely associated with the memory functions present in evolution equations which govern the course of such physical phenomena like non-Debye relaxations or anomalous diffusion. Commonly accepted procedure to mimic memory effects

Topological data analysis provides a new perspective on many problems in the domain of complex systems. Here, we establish the dependency of mean values of functional p-norms of ’persistence landscapes’ on a uniform scaling of the underlying multivariate distribution. Furthermore, we demonstrate that average values of p-norms are decreasing, when the covariance in a system is increasing. To illustrate

The purpose of this paper is twofold. We first provide the mathematical analysis of a dynamic contact problem in thermoelasticity, when the contact is governed by a normal damped response function and the constitutive thermoelastic law is given by the Duhamel-Neumann relation. Under suitable hypotheses on data and using a Faedo-Galerkin strategy, we show the existence and uniqueness of solution for

Financial markets are usually affected by various factors, such as breaking news or the release of important economic data, which would interrupt normal fluctuations and cause the abruptly increasing of volatility. How the financial markets behave under the impact of sudden external stimulations is of great significance for the analysis and prediction of financial prices. In this article, combining

We present a new stochastic model, based on a 0-dimensional version of the well known biogeochemical flux model (BFM), which allows to take into account the temperature random fluctuations present in natural systems and therefore to describe more realistically the dynamics of real marine ecosystems. The study presents a detailed analysis of the effects of randomly varying temperature on the lower trophic

In the paper an elliptic quasi–variational–hemivariational inequality with constraints in a Banach space is studied. First, we apply the Minty technique, the KKM principle and the theory of nonsmooth analysis to establish the solvability of the inequality problem. Then, we employ a generalized penalty and regularization method for the inequality and introduce a family of penalized and regularized problems

The rhythm of the human heart is influenced by the nervous system and certain feedback mechanisms inducing variability to it. This heart rate variation (HRV) is reflected in the data we obtain from an electrocardiogram, data such as the RR intervals which are commonly used in this context. The point of this research area is to find a model capable of describing the HRV. Some of the widely-used techniques

We present an analysis of an extended Rayleigh–Plesset (RP) equation for a three dimensional cell of microorganisms such as bacteria or viruses in some liquid, where the cell membrane in bacteria or the envelope (capsid) in viruses possess elastic properties. To account for rapid changes in the shape configuration of such microorganisms, the bubble membrane/envelope must be rigid to resist large pressures