扩展BVP振子弱周期扰动下的振荡与同步

Oscillation and synchronization of extended BVP oscillator under weak periodic perturbation

针对扩展bonhoeffer-van der pol(BVP)振子易受不确定因素影响的问题,提出了将非线性动力学分析与数值模拟相结合的方法,并考察了弱扰动对混合模式振荡类型和同步行为的影响.根据模拟结果得知,多种类型的混合模式振荡受弱扰动的影响出现了坍塌现象,且从理论上证明了两个耦合bonhoeffer-van der pol振子的膜电压比慢变量到达完全同步时所需的耦合强度要大,在二维参数平面上,膜电压到达同步时所取参数范围应小些.结果表明,与膜电压相比,慢变量更容易达到同步,且变量之间呈现一种线性关系.

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.