Graph-based topological approximation of saddle-node bifurcation in maps : Dedicated to Professor Yasumasa Nishiura for his sixtieth birthday (Far-From-Equilibrium Dynamics)
Zin Arai, Marcio Gameiro, Tomáš Gedeon, Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka · Kyoto University Research Information Repository (Kyoto University) · 2012
An efficient computational framework for obtaining a rigorous combinatorial de- scription of the global dynamics over a large range of parameter values of multiparam- eter nonlinear systems was presented in [1].Because the resulting information is easily queryable and provides important information about the qualitative dynamics, we refer to the output as a database for the dynamics.Such a procedure can only involve a fi- nite number of computations and thus the dynamics can only be represented down to a fixed scale.However, the theory of dynamical systems indicates that nonlinear systems can exhibit different structures at all scales in phase space and that bifurcations of the