This work studies the dynamic of mutualistic ecosystems via Lotka-Volterra model. After exploring the existence and ...

In population dynamics, structural stability measures the ability of an ecosystem to maintain biodiversity under perturbations ...

In this thesis, we study hyperbolicity for deterministic and random nonautonomous dynamical systems and their applications ...

The model transform fits exactly the parameters of a suitable model to empirical or simulated data in each point in time ...

Dynamical systems on graphs allow to describe multiple phenomena from different areas of Science. In particular, many ...

The self-organising global dynamics underlying brain states emerge from complex recursive nonlinear interactions between ...

In this work, we study the continuity and topological structural stability of attractors for nonautonomous random differential ...

Brain dynamics depicts an extremely complex energy landscape that changes over time, and its characterisation is a central ...

In this work we obtain estimates on the fractal dimension of attractors in three different settings: global attractors ...

Finite-dimensional attractors play an important role in finite-dimensional reduction of PDEs in mathematical modelization ...

In this work, we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic ...

This thesis applies the great advances of modern dynamical systems theory (DST) to consciousness. Consciousness, or ...

In this paper we establish a strong comparison principle for a nonautonomous differential inclusion with a forcing term ...

This work deals with the study of the global stability of the system Lokta-Volterra. We focus on the analysis of the global ...

The aim of this project is to study generalized Lotka-Volterra systems applied in ecology. This work is divided in five ...

Informational Structures (IS) and Informational Fields (IF) have been recently introduced to deal with a continuous dynamical ...

In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced ...

Integrated Information Theory (IIT) has become nowadays the most sensible general theory of consciousness. In addition to ...

This work shows The Lotka-Volterra systems like a continuation of the diferential equations studies we have seen in the ...

This work is framed within the field of Dynamical System and their applicaitons to complex networks. In this text we ...

El objetivo principal de este trabajo es el análisis matemático de sistemas de ecuaciones diferenciales que modelan redes ...

En esta tesis estudiamos el comportamiento a largo plazo de sistemas dinámicos multivaluados y aleatorios en términos de ...

In this work we will study the theory of dynamical systems with application to a chemostat. Starting with the autonomous ...

This work shows the attractors theory like a continuation of the differential equations studies we have seen in the subjects ...

The global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour ...

In this paper we prove the equivalence between equi-attraction and continuity of attractors for skew-product semi-flows, ...

The structure of attractors for differential equations is one of the main topics in the qualitative theory of dynamical ...

In this paper, we study the pullback attractor for a general reaction-diffusion system for which the uniqueness of solutions ...

This work is framed within the field of Dynamical Systems and we aim to continue the study of the stability of dynamical ...

In this work, the theory of global attractors for parabolics PDEs is studied. We focus on the reaction-diffusion equations ...

En este trabajo estudiamos la estabilidad estructural topológica para una familia de semigrupos no lineales Th(·) sobre espacios de Banach Xh dependiendo de un parámetro h.

Real phenomena from different areas of Life Sciences can be described by complex networks, whose structure is usually ...

In this paper we describe some dynamical properties of a Morse decomposition with a countable number of sets. In particular, ...

In this paper we study a three dimensional mutualistic model of two plants in competition and a pollinator with cooperative ...

El estudio de los sistemas dinámicos es de gran importancia, ya que están relacionados con fenómenos del mundo real. Los ...

We show that the stochastic flow generated by the 2-dimensional Stochastic Navier-Stokes equations with rough noise on a ...

We define (time dependent) Morse-decompositions for non-autonomous evolution processes (non-autonomous dynamical systems) ...

This paper is devoted to the investigation of the dynamics of non-autonomous differential equations. The description of ...

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like ...

In this paper we introduce the concept of a gradient random dynamical system as a random semiflow possessing a continuous ...

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there ...

In this paper we consider the strongly damped wave equation with time dependent terms utt − u − γ(t) ut + β"(t)ut = f(u), ...

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646–68)) ...

Este trabajo está dividido en dos partes. Una primera en la que se trata la parte teórica de los sistemas dinámicos autónomos ...

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is ...

In this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to ...

This paper is concerned with the existence of pullback attractors for evolution processes. Our aim is to provide results ...

In this paper we study in detail the pullback and forwards attractions to non-autonomous competition Lotka-Volterra system. ...

In this paper we consider a dissipative damped wave equation with non-autonomous damping of the form utt + ¯(t)ut = ¢u + ...

Lotka-Volterra systems are the canonical ecological models used to analyze population dynamics of competition, symbiosis ...

We prove that the asymptotic behaviour of partial differential inclusions and partial differential equations without ...

In this paper we determine the exact structure of the pullback attractors in non-autonomous problems that are perturbations ...

We study the stability of attractors under non-autonomous perturbations that are uniformly small in time. While in general ...

The study of qualitative properties of random and stochastic differential equations is now one of the most active fields ...

The goal of this work is to study the forward dynamics of positive solutions for the nonautonomous logistic equation ut − ...

In a previous paper we introduced various definitions of stability and instability for non-autonomous differential equations, ...

In this paper, we point out the different long-time behaviour of stochastic partial differential equations when one considers ...

We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, ut−Δu = βu−u3, by noise. ...

In this paper we extend the well-known bifurcation theory for autonomous logistic equations to the non-autonomous equation ut ...

The aim of this note is to clarify a misleading statement which appeared in our fi rst paper dealing with the concept of global random attractor for multivalued random dynamical systems, as well as in the subsequent work

We introduce the concept of a monotone multi-valued semi- ow as an order-preserving map. This de nition is motivated by ...

An abstract system of coupled nonlinear parabolic-hyperbolic partial differential equations subjected to additive white ...

We delve deeper into the study of semimartingale attractors that we recently introduced in Allouba and Langa [4] H. Allouba ...

We prove, on one hand, that for a convenient body force with values in the distribution space (H−1(D))d, where D is the ...

Lotka-Volterra systems have been extensively studied by many authors, both in the autonomous and non-autonomous cases. In ...

The goal of this work is to study in some detail the asymptotic behaviour of a non-autonomous Lotka-Volterra model, both ...

Some results on the relationship of the solutions of a stochastic di erential inclusion and the corresponding random di ...

The concept of nonautonomous (or cocycle) attractor has become a proper tool for the study of the asymptotic behaviour of ...

In this paper we study the existence of pullback global attractors for multivalued processes generated by differential ...

There is a vast body of literature devoted to the study of bifurcation phenomena in autonomous systems of differential ...

Uno de los conceptos más importantes para la descripción del comportamiento asintótico de ecuaciones en derivadas parciales ...

Some results on the pathwise exponential stability of the weak solutions to a stochastic 2D-Navier-Stokes equation are ...

We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the ...

In this paper we consider a stochastic differential inclusion with multiplicative noise. It is shown that it generates a multivalued random dynamical system for which there also exists a global random attractor.

The concept of global attractor for stochastic partial differential inclusions has been recently introduced as a joint ...

We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the ...

We study in some detail the structure of the random attractor for the Chafee{Infante reaction{di¬usion equation perturbed ...

Using the relatively new concept of a pullback attractor, we present some results on the existence of attractors for differential equations with variable delay. We give a variety of examples to which our result applies.

We study the asymptotic behaviour of a reaction-diffusion equation, and prove that the addition of multiplicative white ...

Two tracking properties for trajectories on attracting sets are studied. We prove that trajectories on the full phase space ...

The theory of random attracting sets highlights interesting properties of the asymptotic behaviour of some stochastic ...

The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential ...

"En el Capítulo 1, presentamos una síntesis de los resultados básicos sobre atractores globales que pueden encontrarse en ...