A generalized form of the autonomous Bonhoeffer-van der Pol (BVdP) system described by a second-order dynamical system with six independent parameters consistent with its optimal mathematical modeling, instead of three usually used, is investigated. Through its equivalent form, the generalized asymmetric van der Pol-Duffing (GAVdPD) system and the steady states of this system are derived. The analysis show that the system may exhibit one or three steady states when it is driven by an external constant impulse taken as a main control parameter. Domain ranges in which the system can function as well as monostable system as a bistable system are derived. In addition, by means of the theory of Hopf Bifurcation, it appears that there are large possibilities for the system to work as self-sustained oscillator, forced oscillator or other possibilities for which the system does not operate, indicating the richness of this generalized form of the BVdP system. Limit cycle solutions are derived at the neighboring of the Andronov-Hopf Bifurcation points even for large values of the asymmetric parameter. All these results are checked through numerical simulations. Applying these analytical investigations to the electronic circuit executing the dynamics of the basic BVdP system, two distinct working regimes are highlighted, depending on the magnitude of the capacitance with respect to a threshold value function of the characteristic parameters both of the self and of the nonlinear resistance. Through PSPICE simulations the accuracy of these analytical and numerical investigations have been confirmed.

研究了由二阶动力学系统描述的自治Bonhoeffer-van der Pol（BVdP）系统的广义形式，该动力学系统具有六个与其最佳数学模型一致的独立参数，而不是通常使用的三个参数。通过其等效形式，推导了广义不对称范德波尔-达芬（GAVdPD）系统及其稳态。分析表明，当系统受到外部恒定脉冲作为主要控制力时，系统可能会显示一或三个稳态。范围。得出系统可以在其中运行的域范围以及单稳态和双稳态系统。另外，通过霍普夫分叉理论，看来系统有很大的可能性作为自持振荡器，强制振荡器或系统无法运行的其他可能性工作，这表明这种广义形式的丰富性BVdP系统。即使对于较大的非对称参数值，也可以在Andronov-Hopf分叉点的附近导出极限环解。所有这些结果均通过数值模拟进行检查。将这些分析研究应用于执行基本BVdP系统动力学的电子电路，重点介绍了两种不同的工作方式，取决于电容相对于自身和非线性电阻的特征参数的阈值函数的大小。通过PSPICE仿真，已经证实了这些分析和数值研究的准确性。