A generally applicable, automatic method for the efficient computation of a database of global dynamics of a multiparameter dynamical system is introduced. An outer approximation of the dynamics for each subset of the parameter range is computed using rigorous numerical methods and is represented by means of a directed graph. The dynamics is then decomposed into the recurrent and gradient-like parts by fast combinatorial algorithms and is classified via Morse decompositions. These Morse decompositions are compared at adjacent parameter sets via continuation to detect possible changes in the dynamics. The Conley index is used to study the structure of isolated invariant sets associated with the computed Morse decompositions and to detect the existence of certain types of dynamics. The power of the developed method is illustrated with an application to the two-dimensional density-dependent Leslie population model. Large parts of this article is based on our paper published in , which contains more detailed description of the method.
Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2
- Pub Date:
- September 2009
- Computational methods in statistical physics and nonlinear dynamics;
- Numerical simulation;
- solution of equations;
- Stochastic analysis methods