Imagine the following dynamic system, characterized by two stable equilibria (A and B) and an internal saddle point (C) separating its two basins of attraction of A and B.
clear all
syms x y a b c d e f g h i
Fx = ax(x - 1)(d - (fx + c*(i - 1))(y - 1) + g(x - 1) + y*(fx - h + c(i - 1)))
Fy = by(y - 1)(x(h - i*(e + c - fx)) - h(x - 1) + ix(c - f*x))
par = {[a b c d e f g h i], [0.05 0.05 30 20 10 2 5 2.5 0.4]}
The phase plot for the parameters above is as follows.
How can you calculate (possibly even numerically) the only path converging at saddle point C (the one in green)?
Thank you to anyone who will try to help me.