Dynamics analysis and Hamilton energy control of a generalized Lorenz system with hidden attractor
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Hidden attractor can be found in some dynamic systems. More commonly, it can be excited by the stabilized equilibria, or be generated from the systems without equilibria. The generalized Lorenz system transformed from the Rabinovich system is researched by detecting the generating mechanism under different parameters and initial values, and then we have the good fortune to discover that the hidden attractor is coexisting with the states of stabilization, period, chaos, and even transient chaos. At the same time, the Hamilton energy function of the system is given to discuss the energy transform when the system undergoes a series of oscillations. The compositional principle can be used to design a new chaos control method, which is called Hamilton energy control. By numerical simulating, the feedback gain in the present control method is assigned and then controls the system with hidden attractor to expected states effectively. The feature of the control method can be indicated that the Hamilton energy can be detected during the oscillation control processes.
KeywordsHidden attractor Lyapunov exponents Helmholtz’s theorem Hamilton Energy Energy control
The authors gratefully acknowledge Prof. Jun Ma from Lanzhou University of Technology for the constructive suggestions. This work is supported from the National Natural Science Foundation (No. 51408288), China Postdoctoral Science Foundation(No. 2018M633649XB), Natural Science Foundation of Gansu Province, Government of China (No. 17JR5RA096), and Lzjtu (201606) EP support.
Compliance with ethical standards
Conflict of interest
The authors declare no conflict of interest.
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