Related papers: Etude d'un mod\`ele de dynamique des populations

Profiles of static solitons in one-dimensional scalar field theory satisfy the same equations as trajectories of a fictitious particle in multidimensional mechanics. We argue that the structure and properties of the solitons are essentially…

It is shown, under weak conditions, that the dynamical evolution of an important class of large systems of globally coupled, heterogeneous frequency, phase oscillators is, in an appropriate physical sense, time-asymptotically attracted…

The analysis of the long-term behavior of the mathematical model of a neural network constitutes a suitable framework to develop new tools for the dynamical description of nonautonomous state-dependent delay equations (SDDEs). The concept…

We study the influence of stochastic effects due to finite population size in the evolutionary dynamics of populations interacting in the multi-person Prisoner's Dilemma game. This paper is an extension of the investigation presented in a…

Non-autonomous differential equations exhibit a highly intricate dynamics, and various concepts have been introduced to describe their qualitative behavior. In general, it is rare to obtain time dependent invariant compact attracting sets…

Biologists and physicists have a rich tradition of modeling living systems with simple models composed of a few interacting components. Despite the remarkable success of this approach, it remains unclear how to use such finely tuned models…

This study covers an analytical approach to calculate positively invariant sets of dynamical systems. Using Lyapunov techniques and quantifier elimination methods, an automatic procedure for determining bounds in the state space as an…

We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the…

Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…

Lorenz attractors play an important role in the modern theory of dynamical systems. The reason is that they are robust, i.e. preserve their chaotic properties under various kinds of perturbations. This means that such attractors can exist…

We provide a framework for studying the expansion rate of the image of a bounded set under a flow in Euclidean space and apply it to stochastic differential equations (SDEs for short) with singular coefficients. If the singular drift of the…

From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…

We study long-time dynamics of a class of abstract second order in time evolution equations in a Hilbert space with the damping term depending both on displacement and velocity. This damping represents the nonlinear strong dissipation…

In this paper, we present a unified framework of multiple attractors including multistability, multiperiodicity and multichaos. Multichaos, which means that the chaotic solution of a system lies in different disjoint invariant sets with…

It has been shown by Le Jan that, given a memoryless-noise random dynamical system together with an ergodic distribution for the associated Markov transition probabilities, if the support of the ergodic distribution admits locally…

In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins,…

The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…

The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…

For stochastic Hindmarsh-Rose equations with additive noises in the study of neurodynamics, the longtime and global pullback dynamics on a two-dimensional bounded domain is explored in this work. Using the additive transformation and by the…

This work is devoted to further consideration of the Henon map with negative values of the shrinking parameter and the study of transient oscillations, multistability, and possible existence of hidden attractors. The computation of the…