Related papers: Complete synchronization equivalence in asynchrono…
The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…
The dynamics of one-way coupled systems with discrete time is considered. The behavior of the coupled logistic maps is compared to the dynamics of maps obtained using the Poincare sectioning procedure applied to the coupled continuous-time…
The synchronization behavior of delay coupled chaotic smooth unimodal maps over a ring network with stochastic switching of links at every time step is reported in this paper. It is observed that spatiotemporal synchronization never appears…
Existence of different kinds of synchronizations, namely anticipatory, complete and lag type synchronizations (both exact and approximate), are shown to be possible in time-delay coupled piecewise linear systems. We deduce stability…
Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via…
We use symbolic dynamics to study discrete-time dynamical systems with multiple time delays. We exploit the concept of avoiding sets, which arise from specific non-generating partitions of the phase space and restrict the occurrence of…
We introduce a new method for determining the global stability of synchronization in systems of coupled identical maps. The method is based on the study of invariant measures. Besides the simplest non-trivial example, namely two…
Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated map at each…
We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume…
We study the spatio-temporal behavior of simple coupled map lattices with periodic boundary conditions. The local dynamics is governed by two maps, namely, the sine circle map and the logistic map respectively. It is found that even though…
We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. As a result, the numerically…
Several coupled maps models are sketched and reviewed in this short communication. First, a discrete logistic type model that was proposed for the symbiotic interaction of two species. Second, a model of many of these symbiotic species…
We study a family of diffusively coupled chaotic maps on periodic d-dimensional square lattices. Even and odd sub-lattices are updated alternately, introducing an effective delay. As the coupling strength is increased, the system undergoes…
We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the…
A coupled map model for the chaotic phase synchronization and its desynchronization phenomenon is proposed. The model is constructed by integrating the coupled kicked oscillator system, kicking strength depending on the complex state…
We study the synchronization of two chaotic maps with unidirectional (master-slave) coupling. Both maps have an intrinsic delay $n_1$, and coupling acts with a delay $n_2$. Depending on the sign of the difference $n_1-n_2$, the slave map…
Here we show that for coupled-map systems, the length of the transient prior to synchronization is both dependant on the coupling strength and dynamics of connections: systems with fixed connections and with no self-coupling display…
We investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of…
Networks of chaotic units with static couplings can synchronize to a common chaotic trajectory. The effect of dynamic adaptive couplings on the cooperative behavior of chaotic networks is investigated. The couplings adjust to the activities…
We present the linear-stability analysis of synchronised states in coupled time-delay systems. There exists a synchronisation threshold, for which we derive upper bounds, which does not depend on the delay time. We prove that at least for…