Algebraic Systems.

  Specifically, for (2.1) the program can : 

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Compute solution branches.
(Demo ab; Run 1.)

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Locate branch points and automatically compute bifurcating branches.
(Demo pp2; Run 1.)

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Locate Hopf bifurcation points and continue these in two parameters.
(Demo ab; Runs 1 and 5.)

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Locate folds (limit points) and continue these in two parameters.
(Demo ab; Runs 1,3,4.)

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Do each of the above for fixed points of the discrete dynamical system
(Demo dd2.)

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Find extrema of an objective function along solution branches and successively continue such extrema in more parameters.
(Demo opt.)