Adaptive Generalized Function Projective Synchronization in Coupled Time-delayed Systems with Unknown Parameters and Noise Perturbation

Abstract: Noise perturbation and time delay are ubiquitous in both nature and man-made systems, and must be taken into consideration in the design of synchronization. In this paper, a design of adaptive controller and update laws for generalized function projective synchronization in coupled time-delayed systems with unknown parameters and noise perturbation are established. Based on the LaSalle-type invariance for stochastic time-delayed differential equations and adaptive control theory, sufficient conditions guaranteeing generalized function projective synchronization are developed, and the unknown parameters are also estimated. Numerical simulations fully support the analytical results.