Related papers: Chaotifiying continuous-time systems by symmetry
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the instability of each spatial mode (pattern) we…
Quantum groups have a long and fruitful history of applications in integrable systems. Can quantum group symmetries exist in the absence of integrability? We provide an explicit example of a system with quantum group global symmetry which…
We introduce a novel approach for controlling fast chaos in time-delay dynamical systems and use it to control a chaotic photonic device with a characteristic time scale of ~12 ns. Our approach is a prescription for how to implement…
We present a stochastic algorithm for constructing a topologically disordered (i.e., non-regular) spatial lattice with nodes of constant coordination number, the CC lattice. The construction procedure dramatically improves on an earlier…
The problem of separation of an observed sum of chaotic signals into the individual components in the presence of noise on the path to the observer is considered. A noise threshold is found above which high-quality separation is impossible.…
We investigate the phenomenon of chaos synchronization in systems subject to coexisting autonomous and external global fields by employing a simple model of coupled maps. Two states of chaos synchronization are found: (i) complete…
We study how a coupled array of spiking chaotic systems synchronizes to an external driving in a short time. Synchronization means spike separation at adjacent sites much shorter than the average inter-spike interval; a local lack of…
We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity…
In this paper we show that the analysis of the dynamics in localized regions, i.e., sub-systems can be used to characterize the chaotic dynamics and the synchronization ability of the spatiotemporal systems. Using noisy scalar time-series…
Synchronization among globally coupled, chaotic map lattices can be related to stable periodic windows in isolated chaotic maps. This relation provides a simple predictive tool for the understanding of complicated behavior in coupled…
We study a new class of chaotic systems with dynamical localization, where gain or loss mechanisms break the Hermiticity, while allowing for parity-time (PT) symmetry. For a value \gamma_PT of the gain or loss parameter the spectrum…
The presence of a nonattractive chaotic set, also called chaotic saddle, in phase space implies the appearance of a finite time kind of chaos that is known as transient chaos. For a given dynamical system in a certain region of phase space…
A method to synchronize two chaotic systems with anticipation or lag, coupled in the drive response mode, is proposed. The coupling involves variable delay with three time scales. The method has the advantage that synchronization is…
Extracting reliable indicators of chaos from a single experimental time series is a challenging task, in particular, for systems with many degrees of freedom. The techniques available for this purpose often require unachievably long time…
We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of…
A switching dynamical system by means of piecewise linear systems in R^3 that presents multistability is presented. The flow of the system displays multiple scroll attractors due to the unstable hyperbolic focus-saddle equilibria with…
We investigate synchronization between two unidirectionally coupled chaotic multi-feedback Ikeda systems and find both the existence and stability conditions for anticipating, lag, and complete synchronizations.Generalization of the…
This paper deals with adaptive synchronization of chaos in the presence of time-varying communication-delays. We consider two bidirectionally coupled systems that seek to synchronize through a signal that each system sends to the other one…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…