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Low Model Analysis and Synchronous Simulation of the Wave Mechanics

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  • Wenyuan Duan
  • Heyuan Wang
  • Meng Kan

Abstract

The dynamic behavior of a chaotic system in the internal wave dynamics and the problem of the tracing and synchronization are investigated, and the numerical simulation is carried out in this paper. The globally exponentially attractive set and positive invariant set of the chaotic system are studied via constructing the positive definite and radial unbounded Lyapunov function. There are no equilibrium positions, periodic solutions, quasi-period motions, wandering recovering motions, and other chaotic attractors of the system out of the globally exponentially attractive set. Strange attractors can only locate in the globally exponentially attractive set. A feedback controller is designed for the chaotic system to realize the control of the unstable point. The second method of Lyapunov is used to discuss theoretically the rationality of the design of the controller. The driving-response synchronization method is used to realize the globally exponential synchronization. The numerical simulation is carried out by MATLAB software, and the simulation results show that the method is effective.

Suggested Citation

  • Wenyuan Duan & Heyuan Wang & Meng Kan, 2016. "Low Model Analysis and Synchronous Simulation of the Wave Mechanics," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-13, September.
    • Handle: RePEc:hin:jnlmpe:2850651
    DOI: 10.1155/2016/2850651
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