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A non-autonomous conservative system and its reconstitution in integral domain

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Abstract

Non-autonomous conservative system with time-dependent stimulus has rarely been studied in literature. In this paper, we present a two-dimensional non-autonomous conservative system. It belongs to the category of non-Hamiltonian conservative system, and its dynamical properties are uncovered by kinetic and energy-based analyses. Nested chaotic and quasi-periodic motions, which are volume-conservative but not energy-conservative, are observed under different initial conditions. The topological structures of these conservative motions are closely related to the isoenergetic lines of the governing Hamiltonian function. Furthermore, this non-autonomous conservative system is reconstituted in integral domain. Based on the reformed time-varying equilibrium points and isoenergetic lines, the reconstituted conservative motions are further analyzed. Finally, PSIM circuit simulations are performed to verify the reconstituted conservative motions in the integral domain. As can be seen, the characteristics of the volume-conservative motions are thoroughly interpreted in the original and integral state variable domains.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Numbers 51777016, 61801054, and 61601062, and the Natural Science Foundation of Jiangsu Province, China, under Grant Number BK20191451.

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Authors and Affiliations

  1. School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164, China

    Mo Chen, Chao Wang, Huagan Wu, Quan Xu & Bocheng Bao

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  1. Mo Chen
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Correspondence to Bocheng Bao.

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Chen, M., Wang, C., Wu, H. et al. A non-autonomous conservative system and its reconstitution in integral domain. Nonlinear Dyn 103, 643–655 (2021). https://doi.org/10.1007/s11071-020-06115-2

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