Related papers: Synchronization With Positive Conditional Lyapunov…
Synchronization of identical chaotic systems subjected to common noise has been the subject of recent research. Studies on several chaotic systems have shown that, the synchronization is actually induced by the non-zero mean of the noise,…
An aspect of the synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits unstable dimension variability. Unstable dimension…
A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is…
In this paper, a novel scheme for synchronizing four drive and four response systems is proposed by the authors. The idea of multi switching and dual combination synchronization is extended to dual combination-combination multi switching…
We consider a three-dimensional chaotic system consisting of the suspension of Arnold's cat map coupled with a clock via a weak dissipative interaction. We show that the coupled system displays a synchronization phenomenon, in the sense…
The maximum Lyapunov exponent (referred to the mean half-period of phase libration) of the motion in the chaotic layer of a nonlinear resonance subject to symmetric periodic perturbation, in the limit of infinitely high frequency of the…
We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback…
We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for…
We discuss the predictability of a conservative system that drives a chaotic system with positive maximum Lyapunov exponent $\lambda_0$, such as the erratic motion of an asteroid in the gravitational field of two bodies of much larger mass.…
The dynamics of extended many-body systems are generically chaotic. Classically, a hallmark of chaos is the exponential sensitivity to initial conditions captured by positive Lyapunov exponents. Supplementing chaotic dynamics with…
Chaotic systems can be synchronized by linking them to a common signal, subject to certain conditions. However, the presence of multiple driving signals coming from different systems, give rise to novel behavior. The particular case of…
The threshold, or saturation phenomenon of spatially coupled systems is revisited in the light of Lyapunov's theory of dynamical systems. It is shown that an application of Lyapunov's direct method can be used to quantitatively describe the…
We establish that the entropy production rate of a classically chaotic Hamiltonian system coupled to the environment settles, after a transient, to a meta-stable value given by the sum of positive generalized Lyapunov exponents. A…
We consider an array of N Josephson junctions connected in parallel and explore the condition for chaotic synchronization. It is found that the outer junctions can be synchronized while they remain uncorrelated to the inner ones when an…
We propose a quantitative criterion to determine whether the coupled quantum systems can achieve complete synchronization or phase synchronization in the process of analyzing quantum synchronization. Adopting the criterion, we discuss the…
We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an…
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation…
This paper investigates the problem of synchronization for nonlinear systems. Following a Lyapunov approach, we firstly study global synchronization of nonlinear systems in canonical control form with both distributed…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
The phase space trajectories of many body systems charateristic of simple fluids are highly unstable. We quantify this instability by a set of Lyapunov exponents, which are the rates of exponential divergence, or convergence, of initial…