Pragmatical Adaptive Synchronization by Variable Strength Linear Coupling

Abstract

Pragmatical adaptive synchronization only by variable strength linear coupling without using another active control terms which is usually rather complex is studied. Pragmatical synchronization is based on pragmatical theorem of asymptotical stability in which the probability concept is introduced in concept of stability. By pragmatical adaptive synchronization, not only the synchronization of chaotic systems but also the parameter pursuance is accomplished. Furthermore, Lyapunov function derivative in series form is first used in this paper, which is easier to be obtained than the traditional negative sum of the square of error variables. Lorenz system, Duffing system and Flossier system are illustrated examples.