To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.
We present an adaptive control scheme of accumulative error to stabilize the unstable fixed point for chaotic systems which only satisfies local Lipschitz condition, and discuss how the convergence factor affects the convergence and the characteristics of the final control strength. We define a minimal local Lipschitz coefficient, which can enlarge the condition of chaos control. Compared with other adaptive methods, this control scheme is simple and easy to implement by integral circuits in practice. It is also robust against the effect of noise. These are illustrated with numerical examples.
