一类具有周期脉冲的非线性军备竞赛博弈的动力学研究

Research on Dynamics of a Nonlinear Arms Race Game Under Periodic Pulse

针对目前萨珀斯坦模型在设计上存在的不足,对一方受到周期性干扰情况下军备竞赛的稳定性进行研究。将自我约束变量引入萨珀斯坦模型中,研究其对博弈的影响,分析动力学方程平衡点的稳定性,并在此基础上引入周期脉冲函数,运用Floquet理论构造二维离散动力学方程的Poincaré映射,并求出周期解的Floquet乘子。结果表明:改进后的模型的计算结果与Matlab仿真图形吻合,能为进一步深入理解军备竞赛的作用机制提供借鉴。

In allusion to the problem that Saperstein model have deficiencies in the model design, studied the stability of arms race while one part is periodic interfered. Considering a self-restricting variable Saperstein model and then studying the effects of the self-restricting variable, we analyze the stability of equilibrium points of dynamics equations. On the basis of the analysis, considering a periodic pulse functions Saperstein model, we construct the Poincaré map of two dimension discrete dynamics equations, and calculate Floquet multipliers of periodic solutions. The result shows that the improved model’s calculation results agree with Matlab simulation graphics, and it can provides reference to further understand the arms race functional mechanism.