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.

在本文中，通过将两个具有余弦忆阻的理想忆阻器引入经典的三维 (3-D) Colpitts 振荡器模型，构建了一个基于五维 (5-D) 二维忆阻器的 Colpitts 系统。所提出的忆阻 Colpitts 系统具有平面平衡集，并且它们的稳定性在忆阻器初始平面上周期性变化。此外，稳定性分布模式随着系统控制参数的变化而演变。通过采用几种数值方法研究了参数和初始相关行为。数值模拟结果表明，系统轨迹受到起始点周围几个不稳定稳定区域的限制，导致参数和初始偏移增强动力学的产生。此外，通过状态变量的积分变换，建立了具有确定平衡的降维模型。对参数和初始偏移提升动力学进行了理论重构和数值阐述。最后，进行电路综合和 PSIM（功率仿真）仿真以验证上述动态行为。