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We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes in finite time, but the…
There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…
A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…
The evolution of particulate and multiphase systems can transition from dynamic regimes, governed by classical transport equations with well-defined damping coefficients, to anomalously slow relaxation described by rate equations when the…
This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…
We consider the problem of estimating the parameters of a supercritical controlled branching process consistently from a single observed trajectory of population size counts. Our goal is to establish which parameters can and cannot be…
We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider symmetric two-player games with two…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
In this paper we present an influence of discontinuous coupling on the dynamics of multistable systems. Our model consists of two periodically forced oscillators that can interact via soft impacts. The controlling parameters are the…
Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions…
A symmetrical cubic discrete coupled logistic equation is proposed to model the symbiotic interaction of two isolated species. The coupling depends on the population size of both species and on a positive constant $\lambda$, named the…
The affect of demographic stochasticity of a system of globally coupled chaotic maps is considered. A two-step model is studied, where the intra-patch chaotic dynamics is followed by a migration step that coupled all patches; the…
This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
This paper presents a nonlinear dynamical model which consists the system of differential and operator equations. Here differential equation contains a nonlinear operator acting in Banach space, a nonlinear operator equation with respect to…
Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse,…
We consider two models of deterministic active particles in an external potential. In the limit where the speed of a particle is fixed, both models coincide and can be formulated as a Hamiltonian system, but only if the potential is…
In this article we present the modeling of bi-stability view problems described by the activity or firing rates of two interacting population of neurons. Starting from the study of a complex system, the sys-tem of stochastic differential…
In this paper, we first develop a notion of dominated splitting for $\mathbb M(2,\mathbb C)$-sequences and show it is a stable property under $\|\cdot \|_\infty$-perturbation. Then we show an energy parameter belongs to the spectrum of a…