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Complex dynamical behavior of modified MLC circuit

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  • Fu, Shihui
  • Liu, Yuan

Abstract

In this paper, we mainly investigate the complex dynamical behavior of modified MLC circuit. When its external excitation doesn’t equal zero, it is nonautonomous and non-smooth, hence we theoretically give the conditions under which grazing bifurcation occurs and the periodic orbits only lie in some one zone. More complex grazing bifurcations and coexisting attractors are also found by numerical simulation, among which is mainly produced by the symmetry. Grazing bifurcations and doubling-period bifurcations that can induce chaotic motion and some basins of attraction are given in this paper. If the external excitation of this system equal zero, it is a non-smooth autonomous system. For this case, we theoretically analysis its non-smooth bifurcations of equilibrium points and limit cycle bifurcation, which is also verified by numerical simulation.

Suggested Citation

  • Fu, Shihui & Liu, Yuan, 2020. "Complex dynamical behavior of modified MLC circuit," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920308006
    DOI: 10.1016/j.chaos.2020.110407
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    References listed on IDEAS

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    1. Makenne, Y.L. & Kengne, R. & Pelap, F.B., 2019. "Coexistence of multiple attractors in the tree dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 70-82.
    2. Fu, Shihui & Liu, Yuan & Ma, Huizhen & Du, Ying, 2020. "Control chaos to different stable states for a piecewise linear circuit system by a simple linear control," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
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    Cited by:

    1. Jimin Yu & Zeming Zhao & Yabin Shao, 2023. "On Cauchy Problems of Caputo Fractional Differential Inclusion with an Application to Fractional Non-Smooth Systems," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    2. Lijuan Chen & Mingchu Yu & Jinnan Luo & Jinpeng Mi & Kaibo Shi & Song Tang, 2024. "Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity," Mathematics, MDPI, vol. 12(12), pages 1-17, June.

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