Ordinary Differential Equations.

For the ODE (2.2) the program can : 

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Compute families of stable and unstable periodic solutions and compute the Floquet multipliers, that determine stability, along these families. Starting data for the computation of periodic orbits are generated automatically at Hopf bifurcation points.
(Demo ab; Run 2.)

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Locate folds, branch points, period doubling bifurcations, and bifurcations to tori, along families of periodic solutions. Branch switching is possible at branch points and at period doubling bifurcations.
(Demos tor, lor.)

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Continue folds and period-doubling bifurcations, in two parameters.
(Demos plp, pp3.) The continuation of orbits of fixed period is also possible. This is the simplest way to compute curves of homoclinic orbits, if the period is sufficiently large.
(Demo pp2.)

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Do each of the above for rotations, i.e., when some of the solution components are periodic modulo a phase gain of a multiple of $2 \pi$.
(Demo pen.)

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Follow curves of homoclinic orbits and detect and continue various codimension-2 bifurcations, using the HomCont algorithms of ChKu:94 ChKu:94, ChKuSa:95 ChKuSa:95.
(Demos san, mnt, kpr, cir, she, rev.)

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Locate extrema of an integral objective functional along a family of periodic solutions and successively continue such extrema in more parameters.
(Demo ops.)

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Compute curves of solutions to (2.2) on $[0,1]$, subject to general nonlinear boundary and integral conditions. The boundary conditions need not be separated, i.e., they may involve both $u(0)$ and $u(1)$ simultaneously. The side conditions may also depend on parameters. The number of boundary conditions plus the number of integral conditions need not equal the dimension of the ODE, provided there is a corresponding number of additional parameter variables.
(Demos exp, int.)

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Determine folds and branch points along solution families to the above boundary value problem. Branch switching is possible at branch points. Curves of folds can be computed in two parameters.
(Demos bvp, int.)