Related papers: Synchronization of coupled chaotic maps
The establishment of generalized chaotic synchronization in Ginzburg-Landau equations unidirectionally coupled at discrete points of space (local coupling) has been studied. It is shown that generalized syn-chronization regimes are also…
Anticipated synchronisation occurs when a driven dynamical system synchronises with the future state of the driver system to which it is unidirectionally coupled. Previous theoretical and experimental studies have focused on setups with a…
We characterize the synchronization of an array of coupled chaotic elements as a phase transition where order parameters related to the joint probability at two sites obey power laws versus the mutual coupling strength; the phase transition…
Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable…
We examine synchronization between identical chaotic systems. A rigorous criteria is presented which, if satisfied, guarantees that the coupling produces linearly stable synchronous motion. The criteria can also be used to design couplings…
In his classical work, Kuramoto analytically described the onset of synchronization in all-to-all coupled networks of phase oscillators with random intrinsic frequencies. Specifically, he identified a critical value of the coupling…
The properties of functional relation between a non-invertible chaotic drive and a response map in the regime of generalized synchronization of chaos are studied. It is shown that despite a very fuzzy image of the relation between the…
We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each…
Generalized chaotic synchronization regime is observed in the unidirectionally coupled one-dimensional Ginzburg-Landau equations. The mechanism resulting in the generalized synchronization regime arising in the coupled spatially extended…
We study fully synchronized (coherent) states in complex networks of chaotic oscillators, reviewing the analytical approach of determining the stability conditions for synchronizability and comparing them with numerical criteria. As an…
This article provides a self-contained comprehensive review of the phenomenon of synchronization in dynamical systems, with a particular focus on chaotic systems in both continuous-time and discrete-time contexts. Synchronization, initially…
We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of…
We consider regular lattices of coupled chaotic maps. Depending on lattice size, there may exist a window in parameter space where complete synchronization is eventually attained after a transient regime. Close outside this window, an…
We investigate the persistence of synchronization in networks of diffusively coupled oscillators when the coupling functions are nonidentical. Under mild conditions, we uncover the influence of the network interaction structure on the…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…
We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag…
Synchronization is the spontaneous alignment of the dynamics of weakly-coupled oscillators. In addition to temporal dynamics like periodic and chaotic oscillations, also the spatio-temporal dynamics of spatially-extended systems like…
We consider diffusively coupled map lattices with $P$ neighbors (where $P$ is arbitrary) and study the stability of synchronized state. We show that there exists a critical lattice size beyond which the synchronized state is unstable. This…
We analyze the size limits of coupled map lattices with diffusive coupling at the crossover of low-dimensional to high-dimensional chaos. We investigate the existence of standing-wave-type periodic patterns, within the low-dimensional…