正弦函数作用下的Martin过程

Martin Process on Sine Function

为了弥补单纯M artin过程在描述天气、石油和股市行情等变化过程方面的不足,首先通过对正弦函数作用下的M artin过程进行相图分析,发现该系统状态随着参数的变化而变化,同时经过稳定焦点、倍周期分岔,可将其收缩到混沌吸引子上,且这个状态变化过程会重复出现;然后进一步通过计算机从理论上计算了该系统的最大Lyapunov指数,并通过绘制了分岔图定量地说明了该系统具有混沌行为。

In this paper, it is discovered that the state of Martin process on sine function varies with the parameters. The system state varies from steady focus and multiple bifurcation to strange attractors, moreover this process repeats once again. The system is further shown to be chaos quantificationally by computing the largest Lyapunov exponent and drawing phase portrait of this system.