software for continuation and bifurcation problems in ODE

AUTO can do a limited bifurcation analysis of algebraic systems of the form

  f(u,p) = 0,  f,u in Rn

and of systems of ordinary differential equations of the form

  u'(t) = f(u(t),p),  f,u in Rn

subject to initial conditions, boundary conditions, and integral constraints. Here p denotes one or more parameters. AUTO can also do certain continuation and evolution computations for parabolic PDEs. It also includes the software HOMCONT for the bifurcation analysis of homoclinic orbits. AUTO is quite fast and can benefit from multiple processors; therefore it is applicable to rather large systems of differential equations.

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