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The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic,…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
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…
Collective chaos is shown to emerge, via a period-doubling cascade, from quasiperiodic partial synchronization in a population of identical inhibitory neurons with delayed global coupling. This system is thoroughly investigated by means of…
The effect of the chaotic dynamical states of the agents on the coevolution of cooperation and synchronization in a structured population of the agents remains unexplored. With a view to gaining insights into this problem, we construct a…
We study here a model of globally coupled units with adaptive interaction weights which has a delay in the updating rule. Simulations show that the model with such delayed synaptic change exhibits dynamical self-organization of network…
This paper deals with the chaotic oscillator synchronization. A new approach to detect the synchronized behaviour of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series…
We report a design of delay coupling for lag synchronization in two unidirectionally coupled chaotic oscillators. A delay term is introduced in the definition of the coupling to target any desired lag between the driver and the response.…
Formation of a layered structure is studied in a globally coupled map of chaotic units with a plastic coupling strength that changes depending on the states of units globally and an external input. In the parameter region characterized by…
Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they…
We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability…
The appearance of the chaotic synchronization regimes has been discovered for the coupled spatially extended beam-plasma Pierce systems. The coupling was introduced only on the right bound of each subsystem. It has been shown that with…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
This article studies the synchronization problem of complex dynamical networks. The impulsive control method is considered with a novel event-triggered pinning algorithm. Sufficient conditions on the network topology are obtained to ensure…
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…
Synchrony patterns characterize network states in which nodes organize into clusters based on their synchronized dynamics. The synchronized clusters may further exhibit either active or inactive states. The simultaneous invariance of active…
We study convergence in networks of piecewise-smooth (PWS) systems that commonly arise in applications to model dynamical systems whose evolution is affected by macroscopic events such as switches and impacts. Existing approaches were…
Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. If multiple such networks are coupled together, the question arises whether these rhythms will synchronize. We investigate the impact of…