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This paper investigates the asymptotic behaviour of solutions of periodic evolution equations. Starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class…
The existence of a random attractor in H^1(R^3) \times L^2(R^3) is proved for the damped semilinear stochastic wave equation defined on the entire space R^3. The nonlinearity is allowed to have a cubic growth rate which is referred to as…
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…
We study statistical properties of a family of maps acting in the space of integer valued sequences, which model dynamics of simple deterministic traffic flows. We obtain asymptotic (as time goes to infinity) properties of trajectories of…
We treat three cubic recurrences, two of which generalize the famous iterated map $x \mapsto x (1-x)$ from discrete chaos theory. A feature of each asymptotic series developed here is a constant, dependent on the initial condition but…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
Systems evolving under the influence of competing two-body and three-body interactions, are of particular interest in exploring the stability of equilibrium states of strongly interacting many-body system. We present a solvable model based…
A deterministic system of coupled maps is proposed as a model for economic activity among interacting agents. The values of the maps represent the wealth of the agents. The dynamics of the system is controlled by two parameters. One…
In this Article, several aspects of the asymptotic dynamics of finite-dimensional open quantum systems are explored. First, after recalling a structure theorem for the peripheral map, we discuss sufficient conditions and a characterization…
The asymptotic behaviour of deterministic logit dynamics in heterogeneous routing games is analyzed. It is proved that in directed multigraphs with parallel routes, and in series composition of such multigraphs, the dynamics admits a…
We investigate the time evolution of the entropy for a paradigmatic conservative dynamical system, the standard map, for different values of its controlling parameter $a$. When the phase space is sufficiently ``chaotic'' (i.e., for large…
The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a…
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…
It has been known for some time that the topological entropy is a nondecreasing function of the parameter in the real quadratic family, which corresponds to the intuitive idea that more nonlinearity induces more complex dynamical behavior.…
In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the…
The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete for certain parameter regime and lead to significant changes in the long time dynamics of the…
We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial,…
In this paper, we consider the long time asymptotics of multi-time correlation functions for quantum dynamical systems that are sufficiently random to relax to a ``reference state''. In particular, the evolution of such systems must have a…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…