切换系统的分叉图

dhb2000

最近搞个切换系统的分叉图，谁有这方面的程序啊，还有由于是随状态要切换，所以不能用ode45解方程，请问有什么好点的方法

无水1324

现成的程序很少，切换系统还是不怎么懂？是一个非光滑的系统吧

咕噜噜

对呢，什么是切换系统，俺孤陋寡闻，第一次听说

无水1324

有问题还是在这里讨论的好，在群内看的人比较少，楼主现在考虑得怎么样了

chaos2

For switching systems with discontinous boundaries,  the key is to look for "grazing conditions" to get  your bifurcation scenario.

For switching systems to time interval, define your Poincare mappings.

dhb2000

我做的是两个非线性系统当其中状态量满足一定条件时就由一个系统切换到另一个系统，这样在两个系统间循环切换，我是自己编的程，用龙格库塔法解，但是求解都很麻烦，需要很长时间，有谁用ode45解决过这类问题，还有做分岔图很麻烦的

dhb2000

我现在能做的只能是通过自己把参数值慢慢变，然后通过观察法来判断是否是混沌，分岔

chaos2

in your Runge-Kutta integration scheme, you need to embed the Newton-Raphson method to get solution to satisfy the switching boundary condition. Numerically, this problem is relatively simple.

dhb2000

我是直接用判断语句执行的有没问题啊，高手

chaos2

For the first few switching poitns, it should be okay. It is better to set the accurancy about 1.0E-12 or lower. Sorry, I forgot to tell you that you must consider three cases of switchability. (1) grazing flow, (2) sink flow and (3) source flow to the switching boundary. Your system may have a sink flow on the boundary, that is, your system flow will follow your boundary to move. your system may have a source flow on the boundary, that is, the flow will never access the boundary. All the three cases depend upon your parameters. Hope you are luck.