Display Abstract

Title Organization of dissipative flows: R\"{o}ssler model revisited

Name Sergio Serrano
Country Spain
Email sserrano@unizar.es
Co-Author(s) Roberto Barrio and Fernando Blesa
Submit Time 2014-02-25 09:44:01
Special Session 111: Computational dynamics in Hamiltonian and dissipative systems
The R\"{o}ssler model is a well-known problem among low-dimensional flows with chaotic behavior. Apart from regular and chaotic orbits, the R\"{o}ssler system also has unbounded orbits with a transient (chaotic or regular) behavior. This fact makes a theoretical and numerical analysis of this problem more difficult. In this talk, we take R\"{o}ssler model as paradigmatic example to show how the combined use of different numerical and analytical tools provides a deep insight of the organization of the bifurcation structure of the model, the origin of those structures and the mechanisms that lead to different behaviors of the flow. The main techniques that we combine and show in this talk include but not limited to biparametric Lyapunov exponent sweeps, parameter continuation to locate individual bifurcations of periodic and homoclinic orbits, the numerical computation of bounded regions and of different invariant sets.