Synchronization conditions for master-slave reaction diffusion systems

Abstract

In this work we consider the synchronization of two linearly coupled extended chaotic systems with mismatch parameters. We give a quantitative measure of intensity of the coupling necessary to ensure synchronization, as a function of grade of mismatch.

Synchronization Control in Reaction‐Diffusion Systems: Application to Lengyel‐Epstein System

“…and so, simply, we can show that − is a negative definite matrix. Therefore, based on Theorem 2, systems (22) and (23) are globally synchronized. The time evolution of the error system states 1 and 2 , in this case, is shown in Figures 7 and 8.…”

“…For the uncontrolled system (23) (i.e., U 1 = U 2 = 0), if the initial conditions are given by (V 1 (0, ), V 2 (0, )) = ( + 0.2 cos(4 ), 1 + 2 + 0.6 cos(4 )) then the solutions V 1 and V 2 are shown in Figures 3 and 4. The approximation and calculation of the solutions to the Lengyel-Epstein systems given in (22) and (23) are obtained using the Matlab function "pdepe".…”

Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling

“…Our efforts will focus on problem (8)- (9). Concretely, we are interested in solutions such that the driven systems closely track the evolution of the driver systems at least for a finite time interval.…”

“…Among these in [6,7], the authors have considered a pair of unidirectionally coupled systems with a linear term that penalizes the separation between the actual states of the systems. When the coupling function is linear, the synchronization problem has been addressed through different approaches like invariant manifold method via Galerkin's approximations [8], via an abstract formulation using semigroup theory [7,9], or numerically [6].…”

Synchronization results for a class of fractional-order spatiotemporal partial differential systems based on fractional Lyapunov approach

“…The effect of timedelay autosynchronization on uniform oscillations in a reaction-diffusion system has been presented in [23]. Furthermore, generalized synchronization [24], an approach based on semi-group theory [25,26], functional spaces approach [27], the backstepping synchronization approach [28], the graph-theoretic synchronization approach [29], biological signal transmission using synchronous control [30], pinning impulsive synchronization [31], impulsive type synchronization [32], and hybrid adaptive synchronization strategy [33] for coupled reaction-diffusion systems have been introduced. To the best of our knowledge, the study of synchronization behaviors for fractional-order reaction-diffusion systems remains to this day a new and mostly unexplored field.…”