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Dimensionality Reduction Reconstitution for Extreme Multistability in Memristor-Based Colpitts System

Author

Listed:
  • Yunzhen Zhang
  • Zhong Liu
  • Mo Chen
  • Huagan Wu
  • Shengyao Chen
  • Bocheng Bao

Abstract

In this paper, a four-dimensional (4-D) memristor-based Colpitts system is reaped by employing an ideal memristor to substitute the exponential nonlinear term of original three-dimensional (3-D) Colpitts oscillator model, from which the initials-dependent extreme multistability is exhibited by phase portraits and local basins of attraction. To explore dynamical mechanism, an equivalent 3-D dimensionality reduction model is built using the state variable mapping (SVM) method, which allows the implicit initials of the 4-D memristor-based Colpitts system to be changed into the corresponding explicitly initials-related system parameters of the 3-D dimensionality reduction model. The initials-related equilibria of the 3-D dimensionality reduction model are derived and their initials-related stabilities are discussed, upon which the dynamical mechanism is quantitatively explored. Furthermore, the initials-dependent extreme multistability is depicted by two-parameter plots and the coexistence of infinitely many attractors is demonstrated by phase portraits, which is confirmed by PSIM circuit simulations based on a physical circuit.

Suggested Citation

  • Yunzhen Zhang & Zhong Liu & Mo Chen & Huagan Wu & Shengyao Chen & Bocheng Bao, 2019. "Dimensionality Reduction Reconstitution for Extreme Multistability in Memristor-Based Colpitts System," Complexity, Hindawi, vol. 2019, pages 1-12, November.
    • Handle: RePEc:hin:complx:4308549
    DOI: 10.1155/2019/4308549
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    References listed on IDEAS

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    2. Wu, H.G. & Ye, Y. & Bao, B.C. & Chen, M. & Xu, Q., 2019. "Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 178-185.
    3. Chen, M. & Feng, Y. & Bao, H. & Bao, B.C. & Yu, Y.J. & Wu, H.G. & Xu, Q., 2018. "State variable mapping method for studying initial-dependent dynamics in memristive hyper-jerk system with line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 313-324.
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    5. Mo Chen & Yang Feng & Han Bao & Bocheng Bao & Huagan Wu & Quan Xu, 2019. "Hybrid State Variable Incremental Integral for Reconstructing Extreme Multistability in Memristive Jerk System with Cubic Nonlinearity," Complexity, Hindawi, vol. 2019, pages 1-16, June.
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