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.
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