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 a directional region control （DRC） model of thermal diffusion fractal growth with active heat diffusion in three-dimensional space. This model can be applied to predict the space body heat fractal growth and study its directional region control. When the nonlinear interference term and the inner heat source term are generalized functions, the relationship between the particle aggregation probability and the interference terms can be obtained using the norm theory. We can then predict the aggregation form of particles in different regions. When the nonlinear interference terms in the model are expressed as a trigonometric function and its composite function, our simulations show that the DRC method of thermal fractal diffusion is effective and has reference value for the directional control of actual fractal growth systems.
In this paper, we propose a new method to realize drive-response system synchronization control and parameter identification for a class of generalized Julia sets. By means of this method, the zero asymptotic sliding variables are applied to control the fractal identification. Furthermore, the problems of synchronization control are solved in the case of a drive system with unknown parameters, and the unknown parameters of the drive system can be identified in the asymptotic synchronization process. The results of simulation examples demonstrate the effectiveness of this new method. Particularly, the basic Julia set is also discussed.
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.
The aim of this paper is to study complex modified projective synchronization（CMPS） between fractional-order chaotic nonlinear systems with incommensurate orders. Based on the stability theory of incommensurate fractional-order systems and active control method, control laws are derived to achieve CMPS in three situations including fractional-order complex Lorenz system driving fractional-order complex Chen system, fractional-order real Rssler system driving fractional-order complex Chen system, and fractionalorder complex Lorenz system driving fractional-order real Lü system. Numerical simulations confirm the validity and feasibility of the analytical method.
