Critical value of homoclinic bifurcation

[LorenaGr]

Hello,
I hope to find some help.
I have equation:

and I need to find the value of parameter A at which the homoclinic bifurcation occurs.
I know, that in this case A=-0.34, but I solution, how to find it.
Can you help me, what numerical method I should use to find A?

Thank you very much.

 

[nbryan5]

One possible approach would be to use numerical methods such as Newton's method or the bisection method to find the root of the equation, where the root is the value of A at which the homoclinic bifurcation occurs. These methods involve iteratively approximating the root of the equation given an initial guess. You can read more about the different numerical methods here: https://en.wikipedia.org/wiki/Root-finding_algorithm.