Spatio-temporal chaos in duopoly games

Spatio-temporal chaos in a chemotaxis model

In this paper we explore the dynamics of a one-dimensional Keller–Segel type model for chemotaxis incorporating a logistic cell growth term. We demonstrate the capacity of the model to self-organise into multiple cellular aggregations which, according to position in parameter space, either form a stationary pattern or undergo a sustained spatio-temporal sequence of merging (two aggregations coa...

Spatio-temporal Chaos. Errors and Correction

Spatio-temporal Control for Dynamic Routing Games

In this paper, we study dynamic routing games where the decision of an user is spatio-temporal control. Each user ships its demand over time on a shared resource. We investigate the equilibrium of such systems and show the existence and uniqueness of equilibrium. In the second part, we study a stochastic congestion games where there is only one shared resource and the traffic is indivisible. Th...

Spatio-temporal Chaos. 3. Natural Spatio-temporal Measures for Coupled Circle Map Lattices

In a series of three papers, we study the geometrical and statistical structure of a class of coupled map lattices with natural couplings. These are innnite-dimensional analogues of Axiom A systems. Our main result is the existence of a natural spatio-temporal measure which is the spatio-temporal analogue of the SRB measure. In the rst paper we develop a stable manifold theory for such systems ...

Spatio-temporal Chaos. 1. Hyperbolicity, Structural Stability, Spatio-temporal Shadowing and Symbolic Dynamics

In a series of three papers, we study the geometrical and statistical structure of a class of coupled map lattices with natural couplings. These are innnite-dimensional analogues of Axiom A systems. Our main result is the existence of a natural spatio-temporal measure which is the spatio-temporal analogue of the SRB measure. In this paper we develop a stable manifold theory for such systems as ...