Abstract
In this paper, the dynamic behavior and control of chaotic systems with hidden attractors are studied. Firstly, a class of autonomous chaotic systems without the equilibrium point is proposed. Secondly, quantitative analysis methods are applied to explore the dynamic behavior of the new chaotic systems. Then, the Hamilton energy function of the new system is calculated by the Helmholtz theorem and the energy feedback controller is designed. Finally, the effectiveness of the controller is verified by numerical simulations. Compared with the line feedback control, the control effect of Hamilton energy control is better.
Highlights
Since the second half of the twentieth century, nonlinear science has made great development
Marius and Michal [23] proved that the impulsive difference equation can generate hidden attractors; they restrained the chaotic behavior of one-dimensional discrete dynamical systems by using pulse control. e construction of multiple hidden attractors was achieved by Wu et al [24] through a universal pulse control
Based on the above analysis, this paper constructs a new dynamic system without equilibrium points and calculates the Hamilton energy function through the Helmholtz theorem, and an energy feedback controller is designed to control the chaotic system by reducing the energy consumption
Summary
Since the second half of the twentieth century, nonlinear science has made great development. Marius and Michal [23] proved that the impulsive difference equation can generate hidden attractors; they restrained the chaotic behavior of one-dimensional discrete dynamical systems by using pulse control. E Hamiltonian energy functions of some classical chaotic systems were calculated and verified by Sarasola [26,27,28]. In 2005, Sarasola et al [29] proposed chaotic systems with phase-space variable functions and Complexity analyzed the energy flow under different coupling intensities. Based on the above analysis, this paper constructs a new dynamic system without equilibrium points and calculates the Hamilton energy function through the Helmholtz theorem, and an energy feedback controller is designed to control the chaotic system by reducing the energy consumption.
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