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.
Highlights
Chua’s circuit [1] and Colpitts oscillator [2] are two important physical circuits used for generating chaos
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
To solve the abovementioned problem, fluxcharge analysis method [13, 14, 22, 23] for the memristorbased dynamical circuits and state variable mapping (SVM) method [11, 40] for the memristor-based dynamical systems were proposed to achieve an equivalent dimensionality reduction model, leading to the fact that the circuit goes from high-order to low-order or the system goes from highdimensional to low-dimensional
Summary
Chua’s circuit [1] and Colpitts oscillator [2] are two important physical circuits used for generating chaos. To solve the abovementioned problem, fluxcharge analysis method [13, 14, 22, 23] for the memristorbased dynamical circuits and state variable mapping (SVM) method [11, 40] for the memristor-based dynamical systems were proposed to achieve an equivalent dimensionality reduction model, leading to the fact that the circuit goes from high-order to low-order or the system goes from highdimensional to low-dimensional With these methods, the implicit initials in the original circuit or system can be changed into explicitly initials-related circuit/system parameters appearing in the dimensionality reduction model, and multiple stable states can be controlled by changing the initials-related circuit/system parameters [14], upon which the mechanism explanation for initials-dependent dynamics can be realized.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
