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Sine-modulation-based memristive system with initials-boosted plane bifurcation and extreme multistability

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Abstract

Memristor is a special nonlinear element with inner state variable and can give rise to the initial-boosted dynamics in systems built with it. This paper proposes a four-dimensional (4-D) sine-modulation-based memristive system by coupling an ideal memristor into a three-dimension (3-D) linear system. Particularly, the coupling variable sampled from the 3-D linear system is first modulated by the sine function before being imported into the ideal memristor. As a result, the 4-D sine-modulation-based memristive system possesses a discrete plane equilibrium set and exhibits significant initials-boosted plane bifurcation in this plane. By means of theoretical analysis and numerical simulation, the initials-boosted coexisting attractors with extreme multistability are also uncovered. Finally, a physical circuit for the 4-D sine-modulation-based memristive system is designed and corresponding circuit simulations are executed by the Power Simulation (PSIM) software.

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Acknowledgements

This work was supported by National Natural Science Foundations of China under Grant Nos. 12172066, 51607013, and 61801054, the Qinglan Project of Jiangsu Province of China, the Scientific Research Foundation of Jiangsu Provincial Education Department, China, under Grant No. 21KJB510001, the Natural Science Foundation of Jiangsu Province, China, under Grant No. BK20191451.

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Authors and Affiliations

  1. School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164, People’s Republic of China

    H. Wu, Y. Zhang, M. Chen & Q. Xu

Authors
  1. H. Wu
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  2. Y. Zhang
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  3. M. Chen
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  4. Q. Xu
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Contributions

The authors declare that each of the four authors equally contributed to both the scientific contents and writing of this manuscript.

Corresponding author

Correspondence to Q. Xu.

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Wu, H., Zhang, Y., Chen, M. et al. Sine-modulation-based memristive system with initials-boosted plane bifurcation and extreme multistability. Eur. Phys. J. Spec. Top. 231, 3019–3027 (2022). https://doi.org/10.1140/epjs/s11734-022-00641-3

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