¹Institute of software, School of Statistics and Applied Mathematics, Fudan University, Shanghai 201203, China.
²Jiangsu Zhongtian technology Software Technology Co., Ltd., Nantong 226000, China.

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Abstract—A new chaotic system with constant Lyapunov exponent spectrum is presented, two system parameters of which remain constant exponent characteristics. The basic dynamic properties of the new system are analyzed by Poincar section, Lyapunov exponent and dimension and the signal power spectrum. Based on the Lyapunov exponent spectrum, bifurcation diagrams and state variable amplitude with respect to system parameters show that the new system has two parameters with globally nonlinear modulation characteristic. Based on the Lyapunov stability theory and the improvement of the traditional method, through constructing a Lyapunov function with containing a positive constant that the complete synchronization with single controllers are achieved by means of nonlinear active feedback, adaptive, backstepping and passive control theory, respectively. And the designed single controllers are verified via numerical simulation. Because of single controller, synchronous switch circuit consists of four synchronization schemes is implemented, which further validate the correctness and practicability of the single controllers.

Index Terms—Chaotic system, Lyapunov exponent, synchronization, single controller, circuit implementation.

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Cite: Jian Jiang, Qing-Qing Wu, "A New Three-Dimensional Chaotic System with Constant Exponent Spectrum: Analysis, Synchronization and Circuit Implementation," Journal of Software vol. 11, no. 5, pp. 494-511, 2016.