Based on the construction pattern of Chen, Liu and Qi chaotic systems, a new threedimensional (3D) chaotic system is proposed by developing Lorenz chaotic system. It’s found that when parameter e varies, the Lyapunov exponent spectrum keeps invariable, and the signal amplitude can be controlled by adjusting e. Moreover, the horseshoe chaos in this system is investigated based on the topological horseshoe theory.

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In this paper, the issue of synchronization and parameter identification for a class of chaotic and hyperchaotic systems is discussed. Based on the theories of adaptive control and impulsive control, a synchronization scheme is developed to achieve complete synchronization and parameter identification of a class of chaotic and hyperchaotic systems for the first time. Sufficient conditions are derived to synchronize the systems with different impulse distances. The bounds of the stable regions are also estimated. Numerical examples are presented to demonstrate the effectiveness of the proposed controllers and identifiers.