Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling. (7th December 2017)

• Record Type: Journal Article
• Authors: Acosta, A.; García, P.; Leiva, H.; Merlitti, A.
• Other Names: Wang Peiguang Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2017(2017)
• Publication Date: 2017-12-07
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2017/1946304
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : We consider two reaction-diffusion equations connected by one-directional coupling function and study the synchronization problem in the case where the coupling function affects the driven system in some specific regions. We derive conditions that ensure that the evolution of the driven system closely tracks the evolution of the driver system at least for a finite time. The framework built to achieve our results is based on the study of an abstract ordinary differential equation in a suitable Hilbert space. As a specific application we consider the Gray-Scott equations and perform numerical simulations that are consistent with our main theoretical results.