Lag synchronization of structurally nonequivalent chaotic systems with time delays (Q876900)

The authors investigate the synchronization of a class of structurally nonequivalent chaotic systems with time delay \[ \begin{cases} & \dot x=-\alpha_1 x+f(x_t),\\ &\dot y=-\alpha_2 y+g(y_t)+f(x_{t-\tau})- g(x_{t-\tau})+kx_\tau,\\ & \triangle y=y(t^+_k)-y(t^-_k)=-B_k[x(t_k-\tau)-y(t_k^-)]. \end{cases} \] Let \(e(t)=x(t-\tau)-y(t)\). The authors get a new system which is satisfied by \(e(t)\). Then, the uniformly asymptotical stability of the origin of the new system is proved by using Lyapunov-like function method. The stability implies the synchronization of the original system. Finally, some applications and examples are given.