Stability Analysis of Periodic Solutions of Bonhoeffer–Van Der Pol System with Applied Impulse

In this paper, the stability analysis of periodic solutions of Bonhoeffer–van der Pol system with applied impulse was investigated using Lyapunov direct method. Through the use of appropriate values of the control parameters, three equilibria points and periodic solutions of the system were obtained. A Lyapunov candidate which depended on the parameters was constructed. Hence, we concluded that the equilibria points have different regions of stability and instability of the system in which the two regions were found to be stable and the other region was unstable. Furthermore, Mathcad software was used to analyze the behavior of the system, thereby improving known results in literature.