Synchronization and Impulsive Control of Some Parabolic Partial Differential Equations

Abstract

Novel equi-attractivity in large generalized non-linear partial differential equations were performed for the impulsive control of spatiotemporal chaotic. Attractive solutions of these general partial differential equations were determined. A proof for existence of a certain kind of impulses for synchronization such that the small error dynamics that is equi-attractive in the large is established. A comparative study between these general non-linear partial differential equations and the existent reported numerical theoretical models was developed. Several boundary conditions were given to confirm the theoretical results of the general non-linear partial differential equations. Moreover, the equations were applied to Kuramoto–Sivashinsky PDE′s equation; Grey–Scott models, and Lyapunov exponents for stabilization of the large chaotic systems with elimination of the dynamic error.