# MatCont for Homotopy Method

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FBBVC on 22 Apr 2020
Commented: Andrew Newell on 29 Apr 2020
Hello,
has anybody managed or can give some advice how to apply the homotopy method within matcont? My goal is to follow the path of solution x (equilibrium) to a linear shifted function H(x, t) = F(x(t)) − (1 − t)F(x0). During that path, I want to encounter possible bifurcatin points. F is a different function, that outputs just some kind of vector to the given x(t).
MatCont seems to be perfect for that application but it seems like it only handles differential equations. How can I adapt it to work with a simple (system of) equations?

Andrew Newell on 24 Apr 2020
Edited: Andrew Newell on 24 Apr 2020
The primary purpose of MatCont (which is a GUI front end for Cl_MatCont) is to analyze solution curves of the form . These may be equilibrium solutions of an ODE system and that is how MatCont expects you to enter it. So one approach would just be to pretend it's an ODE and then find the equilibrium solutions.
MatCont creates a curve file and then uses Cl_MatCont to solve for the curve and its critical points. So another approach is to create the curve file yourself and run Cl_MatCont. You can then formulate it explicitly as an equilibrium curve instead of an ODE. This is more work and requires a much greater familiarity with Cl_MatCont, but it's a better approach if you're planning to solve a particular kind of problem many times. If you want to do that, I recommend reading the manual. In the first example it shows you how to solve and there is no ODE.
Andrew Newell on 29 Apr 2020