Parameter and initial offset boosting dynamics in two-memristor-based Colpitts system

In this paper, a five-dimensional (5-D) two-memristor-based Colpitts system is constructed by introducing two ideal memristors with cosine memductance into the classical three-dimensional (3-D) Colpitts oscillator model. The proposed memristive Colpitts system possesses a plane equilibrium set and their stabilities are periodically varied on the memristor initial plane. Moreover, the stability distribution patterns are evolved with the change of system control parameters. The parameter- and initial-dependent behaviors are investigated by employing several numerical methods. The numerically simulated results indicate that the system trajectories are confined by several unstable stability regions around the initiating point, leading to the generation of parameter and initial offset boosting dynamics. Furthermore, a dimensionality reduction model with determined equilibrium is formulated through integral transformation of state variables. The parameter and initial offset boosting dynamics is reconstituted theoretically and expounded numerically. Finally, circuit synthesis and PSIM (power simulation) simulations are carried out to validate the abovementioned dynamical behaviors.