Stability And Persistence Of Diffusively Coupled Lattice Oscillators With Time Lag

Abstract

This is a study of oscillators each with an asymptotically stable limit cycle coupled a11- to-all by a linear diffusive path with a time lag. The dessert at ion contains four parts: the introduction. literature review. and three other chapters. The introduction deals with the svnchronization phenomena, Normal Hyperbolicity, Generalized Lyapunov Exponents and tho Basic Theory of DDEs. In chapter two, we review what has been done in systems of' oscillator with/without a delay in the coupling. We also review what is known in the computation of maximum lyapunov exponents of system with a coupling involving a time lag. In chapter 3, we establish the conditions for :'3tability and persistence or robustness of synchronized state. Chapter four is the conclusion.