DERPER - An algorithm for the continuation of periodic solutions in ordinary differential equations
An algorithm for the continuation of periodic solutions of ODE was derived and tested. The algorithm is based on the shooting method and a standard continuation algorithm. Variational variables are used to compute the Jacobi matrix. The starting point on the periodic orbit is adaptively changed in the algorithm by fixing one component of the solution. Stability of periodic solutions along the continuous branch of solutions is determined by computing characteristic multipliers. Without difficulty the algorithm crosses limit points and at bifurcation points, double-period bifurcation points, and points of tori bifurcation it proceeds along the original branch of solutions. The usefulness of the algorithm is demonstrated in two examples. One of them describes two stirred tank reactors with mutual mass exchange, the other one is the Lorenz model of turbulence.
scientific article; zbMATH DE number 3919697
scientific article