Compound Synchronization of Four Chaotic Complex Systems

The chaotic complex system is designed from the start of the chaotic real system. Dynamical properties of a chaotic complex system in complex space are investigated. In this paper, a compound synchronization scheme is achieved for four chaotic complex systems. According to Lyapunov stability theory and the adaptive control method, four chaotic complex systems are considered and the corresponding controllers are designed to realize the compound synchronization scheme. Four novel design chaotic complex systems are given as an example to verify the validity and feasibility of the proposed control scheme.

A New Fractional-Order Chaotic Complex System and Its Antisynchronization

We propose a new fractional-order chaotic complex system and study its dynamical properties including symmetry, equilibria and their stability, and chaotic attractors. Chaotic behavior is verified with phase portraits, bifurcation diagrams, the histories, and the largest Lyapunov exponents. And we find that chaos exists in this system with orders less than 5 by numerical simulation. Additionally, antisynchronization of different fractional-order chaotic complex systems is considered based on the stability theory of fractional-order systems. This new system and the fractional-order complex Lorenz system can achieve antisynchronization. Corresponding numerical simulations show the effectiveness and feasibility of the scheme.

PROJECTIVE SYNCHRONIZATION IN CHAOTIC COMPLEX SYSTEM WITH TIME DELAY

A projective synchronization of chaotic complex system was investigated. First, the cross projective synchronization (the real part and the imaginary part synchronize up to different scaling factors, respectively) in coupled partially linear complex nonlinear dynamic system was realized without adding any control term. Then, we investigated the substantial conditions of projective synchronization of chaotic complex systems on whole state variable with time delay. The adaptive controllers were designed. Moreover, numerical simulations were given to confirm the analytical results.