Related papers: Exploring the Collective Behavior on the One-dimen…
We demonstrate the phenomenon of stochastic resonance (SR) for discrete-time dynamical systems. We investigate various systems that are not necessarily bistable, but do have two well defined states, switching between which is aided by…
We consider the problem of local correlations in the kicked, dual-unitary coupled maps on D-dimensional lattices. We demonstrate that for D>=2, fully dual-unitary systems exhibit ultra-local correlations: the correlations between any pair…
A system of coupled two logistic maps, one periodic and the other chaotic, is studied. It is found that with the variation of the coupling strength, the system displays several curious features such as the appearance of quadrupling of…
The phenomenology of a system of two coupled quadratic maps is studied both analytically and numerically. Conditions for synchronization are given and the bifurcations of periodic orbits from this regime are identified. In addition, we show…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice, with parameters determined by the probability distribution…
Several theorems are demonstrated that determine the sufficient conditions for the existence of synchronized states (periodical and chaotic) and also of travelling waves in a CML. Also are analytically proven the existence of…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
In this letter we study chaotic dynamical properties of an asymmetrically coupled one-dimensional chain of maps. We discuss the existence of coherent regions in terms of the presence of defects along the chain. We find out that temporal…
A simple construction is presented, which generalises piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature,…
Recently, highly resolved experiments and simulations have provided detailed insight into the dynamics of turbulent pipe flow. This has revived the interest to identify mechanisms that generate chaotic transients with super-exponential…
We explore the chaotic dynamics of a large one-dimensional lattice of coupled maps with diffusive coupling of varying strength using the covariant Lyapunov vectors (CLVs). Using a lattice of diffusively coupled quadratic maps we quantify…
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 study the existence of chimera states, i.e. mixed states, in a globally coupled sine circle map lattice, with different strengths of inter-group and intra-group coupling. We find that at specific values of the parameters of the CML, a…
We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes…
By choosing a dynamical system with d different couplings, one can rearrange a system based on the graph with given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a…
We investigate the synchronization phenomenon in coupled chaotic map lattices where the couplings decay with distance following a power-law. Depending on the lattice size, the coupling strength and the range of the interactions, complete…
A method to predict the emergence of different kinds of ordered collective behaviors in systems of globally coupled chaotic maps is proposed. The method is based on the analogy between globally coupled maps and a map subjected to an…
We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we…