Two kinds of synchronization for hyperchaotic system as well as its applications

This paper is mainly concerned with the issues of two kinds of synchronization for a class of hyperchaotic systems, i.e., complete synchronization, and coexistence of synchronization and anti-synchronization. Two adaptive control laws with suitable state feedbacks are designed to realize the complete synchronization, and coexistence of synchronization and anti-synchronization for such hyperchaotic systems, and simple yet generic criteria for determining two issues of synchronization are derived throughout our analysis procedures, respectively. It is demonstrated that the approaches developed here further extend the ideas and techniques presented in existing literature, and so they are also convenient to implement in practice. Furthermore, an application toward a secure communication scheme based on coupled hyperchaotic systems is presented. Finally, numerical simulations are given to demonstrate the correctness and the effectiveness of the theoretical results.