[SciPy-user] integrate ODE to steady-state?
Tue Jun 24 20:05:23 CDT 2008
I agree with Rob Clewley's approach. I suspect that finding the zeros of the vector field (f(x)) is the best way to go. Integration is harder and still leaves the problem of multiple equilibria. This is often expressed as finding multiple basins of attraction (each initial condition of which goes to a different equilibrium point). You may have an additional problem in that you want to find the stability of the equilibrium points. If you want a point that a system will stay at even under the influence of some local noise or perturbations, then once you find the equilibrium points, you want to determine their stability. This is done quite easily by evaluating the Jacobian of the vector field (the matrix which is the "gradient" of the vector field: d f(x)/ dx, where f and x are vectors of the same dimension). You then find the eigenvalues of the Jacobian. If all are negative, you have a stable equilibrium. If one if positive, you have an unstable
equilibrium and the actual system will probably *not* ever end up there. I hope that's clear and that helps. Your problem is only as hard as the f(x) is complex and nonlinear. It is not an ODE integration problem, really.
-- Lou Pecora, my views are my own.
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