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| 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. |
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