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

Yunzhen Zhang, Zhong Liu, Mo Chen, Huagan Wu, Shengyao Chen and Bocheng Bao

Complexity, 2019, vol. 2019, 1-12

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.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:4308549

DOI: 10.1155/2019/4308549

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