Synchronization in coupled time-delayed systems with parameter mismatch and noise perturbation

Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rössler System

In this paper, using the Poincaré section of the flow we numerically verify a generalization of a Pesin-like identity at the chaos threshold of the Rössler system, which is one of the most popular three-dimensional continuous systems. As Poincaré section points of the flow show similar behavior to that of the logistic map, for the Rössler system we also investigate the relationships with respect to important properties of nonlinear dynamics, such as correlation length, fractal dimension, and the Lyapunov exponent in the vicinity of the chaos threshold.

Effects of noise on the outer synchronization of two unidirectionally coupled complex dynamical networks

We study the effect of noise on the outer synchronization between two unidirectionally coupled complex networks and find analytically that outer synchronization could be achieved via white-noise-based coupling. It is also demonstrated that, if two networks have both conventional linear coupling and white-noise-based coupling, the critical deterministic coupling strength between two complex networks for synchronization transition decreases with an increase in the intensity of noise. We provide numerical results to illustrate the feasibility and effectiveness of the theoretical results.

Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies

In this paper, the finite-time stochastic outer synchronization between two different complex dynamical networks with noise perturbation is investigated. By using suitable controllers, sufficient conditions for finite-time stochastic outer synchronization are derived based on the finite-time stability theory of stochastic differential equations. It is noticed that the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the settling time is also numerically demonstrated.

Practical time-delay synchronization of a periodically modulated self-excited oscillators with uncertainties

This paper studies time-delay synchronization of a periodically modulated Duffing Van der Pol (DVP) oscillator subjected to uncertainties with emphasis on complete synchronization. A robust adaptive response system is designed to synchronize with the uncertain drive periodically modulated DVP oscillator. Adaptation laws on the upper bounds of uncertainties are proposed to guarantee the boundedness of both the synchronization error and the estimated feedback coupling gains. Numerical results are presented to check the effectiveness of the proposed synchronization scheme. The results suggest that the linear and nonlinear terms in the feedback coupling play a complementary role in increasing the synchronization regime in the parameter space of the synchronization manifold. The proposed method can be successfully applied to a large variety of physical systems.