Bifurcations in nonlinear dynamical systems are related to qualitative changes in the dynamics of the system when a critical threshold for some system parameters is crossed.
Our investigations include:
- Quasiperiodic attractors and their bifurcations: transition to chaos via the destruction of tori
- Crises as bifurcations of chaotic attractors
- Basin boundary metamorphoris
We develop algorithms for the qualitative analysis of dynamical systems (CANDYS/ QA: a program system for numerical bifurcation analysis) and computation of the topological entropy.
Stable final states with smoooth boundaries
Same system with slightly changed parameters exhibits fractal basin boundaries