Abstract
This paper presents a new continuous-time four-dimensional autonomous system based on Lorenz system. We analyze the dissipation, equilibrium, and Lyapunov exponents of the system. Lyapunov exponent spectrum demonstrates that the system possesses rich dynamic behaviors if the parameters of the system vary. In a large range of parameters, the system is hyperchaotic. By using fast terminal sliding mode control method, the synchronization of two different chaotic systems is studied. Synchronization between the new system and hyperchaotic Chen system with noise perturbation is illustrated. Simulation results verify the effectiveness of the proposed method.
Highlights
Since Lorenz first discovered the chaotic attractor [1] in 1963, many new chaotic systems have been found, and there is a lot of interesting work on the study of chaotic systems, such as Rossler system [2], Genesio system [3], Chen system [4], Lü system [5, 6], Liu system [7], and Qi system [8]
Terminal sliding mode control is an effective approach for chaotic synchronization [25, 26]
The diagrams of the synchronized states, the state errors and the controllers of the new system and hyperchaotic Chen system are presented as Figures 9, 10, and 11
Summary
Since Lorenz first discovered the chaotic attractor [1] in 1963, many new chaotic systems have been found, and there is a lot of interesting work on the study of chaotic systems, such as Rossler system [2], Genesio system [3], Chen system [4], Lü system [5, 6], Liu system [7], and Qi system [8]. These chaotic systems have unique positive Lyapunov exponent.
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