I have an 8D nonlinear ODE system and I would like to find all the fixed points(that is, dy/dt=0). Since the dimension is high, it is not pratical to plot the nullclines and observe the fixed points. If I use MATLAB to solve the equations, it seems that MATLAB can only help me find the fixed points near the initial value given by me. Then I need to adjust the initial value to find all the possible fixed points. Due to the high dimension, it seems arduous to use things like for-loop to confirm that all initial values have been tested. And due to the nonlinearity and the high dimension, it is hard for me to find the fixed points analytically.
Are there clever approches to find all the fixed points? Thanks!
Could you construct some coordinate transformations to reduce the problem DoF, without any loss of generality, which might be recovered later as per your real need? If possible, conventional stability analyses could be applicable.
P. K. Karmakar thank you for your advice! Due to the structure of my problem, it works to reduce the dimension. In fact, I transform it into the relationship between two factors and happily the nullcline can be drawn. Thanks again!
Safa Aouinti Thank you for your wonderful reference! The ode network mentioned in the paper does give me some inspiration.
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