Related papers: Chaos synchronization: a review
We consider complete synchronization of identical maps coupled through a general interaction function and in a general network topology where the edges may be directed and may carry both positive and negative weights. We define mixed…
We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the…
Chaotic iterations have been introduced on the one hand by Chazan, Mi- ranker [6] and Miellou [10] in a numerical analysis context, and on the other hand by Robert [12] and Pellegrin [11] in the discrete dynamical systems frame- work. In…
Hair cells of the auditory and vestibular systems display astonishing sensitivity, frequency selectivity, and temporal resolution to external signals. These specialized cells utilize an internal active amplifier to achieve highly sensitive…
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…
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…
Recent studies show indication of the effectiveness of synchronization as a data assimilation tool for small or meso-scale forecast when less number of variables are observed frequently. Our main aim here is to understand the effects of…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
The linear response of synchronized chaotic units with delayed couplings and feedback to small external perturbations is investigated in the context of communication with chaos synchronization. For iterated chaotic maps, the distribution of…
Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In this article…
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…
This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result…
The study of synchronization of coupled systems is currently undergoing a major surge fueled by recent discoveries of new forms of collective dynamics and the development of techniques to characterize a myriad of new patterns of network…
We show the first solvable chaotic synchronization model of unidirectionally coupled dynamical systems. We establish a new interpretation of the conditional Lyapunov exponent that characterizes chaotic synchronization completely. Moreover,…
A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient…
The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator…
"Synchronization of two dynamical systems" is the term used to describe the phenomenon when two or more systems gradually change their states or behaviors to become similar or identical. This can happen in a lot of fields, such as physics,…
We consider synchronization of coupled dynamical systems when different types of interactions are simultaneously present. We assume that a set of dynamical systems are coupled through the connections of two or more distinct networks (each…
We study chaos synchronization between Josephson junctions governed by a central junction with a time delay and demonstrate with numerical simulations the possibility of high quality synchronization. The results are important for obtaining…
A novel viewpoint, i.e., adaptive synchronization, is proposed to explore collective rhythm observed in many complex, self-organizing systems. We show that a simple adaptive coupling is able to tip arrays of oscillators towards collective…