Related papers: Collective Behavior of Coupled Chaotic Maps
Lattice models of coupled dynamical systems lead to a variety of complex behaviors. Between the individual motion of independent units and the collective behavior of members of a population evolving synchronously, there exist more…
The phase ordering dynamics of coupled chaotic bistable maps on lattices with defects is investigated. The statistical properties of the system are characterized by means of the average normalized size of spatial domains of equivalent spin…
Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of "causal"…
We show, using generic globally-coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting…
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical…
Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning…
Phase mixing of chaotic orbits exponentially distributes these orbits through their accessible phase space. This phenomenon, commonly called ``chaotic mixing'', stands in marked contrast to phase mixing of regular orbits which proceeds as a…
Many dynamical systems of different complexity, e.g. 1D logistic map, the Lorentz equations, or real phenomena, like turbulent convection, show chaotic behaviour. Despite huge differences, the dynamical scenarios for these systems are…
We study a one-parameter family of quadratic maps, which serves as a template for interior point methods. It is known that such methods can exhibit chaotic behavior, but this has been verified only for particular linear optimization…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
In our previous investigations, we have developed the renormalization group method to $p$-adic models on Cayley trees, this method is closely related to the investigation of $p$-adic dynamical systems associated with a given model. In this…
Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective…
We investigate the spatiotemporal dynamics of a network of coupled chaotic maps, with varying degrees of randomness in coupling connections. While strictly nearest neighbour coupling never allows spatiotemporal synchronization in our…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic…
We investigate the emergence of a collective periodic behavior in a frustrated network of interacting diffusions. Particles are divided into two communities depending on their mutual couplings. On the one hand, both intra-population…
Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in…
The field of quantum chaos originated in the study of spectral statistics for interacting many-body systems, but this heritage was almost forgotten when single-particle systems moved into the focus. In recent years new interest emerged in…
We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($\alpha$), that can vary from first-neighbors to…
Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The…