Geodesic
Dependence of hidden attractors on non-linearity and Hamilton energy in a class of chaotic system
Kybernetika, Tome 54 (2018) no. 4, pp. 648-663 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Non-linearity is essential for occurrence of chaos in dynamical system. The size of phase space and formation of attractors are much dependent on the setting of nonlinear function and parameters. In this paper, a three-variable dynamical system is controlled by different nonlinear function thus a class of chaotic system is presented, the Hamilton function is calculated to find the statistical dynamical property of the improved dynamical systems composed of hidden attractors. The standard dynamical analysis is confirmed in numerical studies, and the dependence of attractors and Hamilton energy on non-linearity selection is discussed. It is found that lower average Hamilton energy can be detected when intensity of nonlinear function is enhanced. It indicates that non-linearity can decrease the energy cost triggering for dynamical behaviors.
Non-linearity is essential for occurrence of chaos in dynamical system. The size of phase space and formation of attractors are much dependent on the setting of nonlinear function and parameters. In this paper, a three-variable dynamical system is controlled by different nonlinear function thus a class of chaotic system is presented, the Hamilton function is calculated to find the statistical dynamical property of the improved dynamical systems composed of hidden attractors. The standard dynamical analysis is confirmed in numerical studies, and the dependence of attractors and Hamilton energy on non-linearity selection is discussed. It is found that lower average Hamilton energy can be detected when intensity of nonlinear function is enhanced. It indicates that non-linearity can decrease the energy cost triggering for dynamical behaviors.
DOI : 10.14736/kyb-2018-4-0648
Classification : 37B25, 37L30
Keywords: Helmholtz theorem; chaos; hidden attractor; bifurcation; Hamilton energy 
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     title = {Dependence of hidden attractors on non-linearity and {Hamilton} energy in a class of chaotic system},
     journal = {Kybernetika},
     pages = {648--663},
     year = {2018},
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Zhang, Ge; Wang, Chunni; Alsaedi, Ahmed; Ma, Jun; Ren, Guodong. Dependence of hidden attractors on non-linearity and Hamilton energy in a class of chaotic system. Kybernetika, Tome 54 (2018) no. 4, pp. 648-663. doi: 10.14736/kyb-2018-4-0648

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