Oscillation and synchronization of extended BVP oscillator under weak periodic perturbation

Aiming at the problem that the extended bonhoeffer-van der pol oscillator is easily affected by uncertainty factors, a method in combination with both nonlinear dynamics analysis and numerical simulation was proposed, and the influence of weak perturbation on the mixed-mode oscillation type and synchronization behavior was investigated. According to the simulated results, it is noted that the collapse phenomenon appears because the mixed-mode oscillation in several types is affected by the weak perturbation. It is theoretically proved that the coupled strength needed to reach the complete synchronization for the membrane voltage of two coupled bonhoeffer-van der pol oscillators is larger than that for the slow variable. On a 2D-parameter plane, the parameter range for the membrane voltage to reach the complete synchronization should be smaller. The results indicate that compared with the membrane voltage, the slow variable is easier to achieve the synchronization. Furthermore, a linear relationship between the variables is presented.