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Homoclinic chaos in the Rössler model
Semyon Malykh1, Yuliya Bakhanova1, Alexey Kazakov1
1National Research University Higher School of Economics, 25/12 Bolshaya Pecherskaya Ulitsa, 603155 Nizhny Novgorod, Russia.
Chaos (Woodbury, N.Y.)
|December 2, 2020
Summary
This study investigates the origins of homoclinic chaos in the Rössler model, revealing how Shilnikov saddle-foci bifurcations shape chaotic dynamics and attractors using computational methods.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Mathematical Modeling
Background:
- The Rössler model, proposed in 1976, is a foundational 3D system for studying chaotic behavior.
- Homoclinic chaos and Shilnikov bifurcations are key phenomena in understanding complex dynamical systems.
Purpose of the Study:
- To investigate the origin of homoclinic chaos in the Rössler model.
- To analyze the role of Shilnikov saddle-foci bifurcations in global bifurcation unfolding.
- To understand the transformations of chaotic attractors within the model.
Main Methods:
- Application of computational methods, including interval maps.
- Utilizing a symbolic approach tailored to the Rössler model.
- Scrutiny of homoclinic bifurcations and detection of chaotic regions.
Main Results:
- Detailed analysis of convoluted bifurcations of Shilnikov saddle-foci.
- Identification of how these bifurcations influence the global dynamics.
- Mapping of regions exhibiting stable and chaotic dynamics in the parameter space.
Conclusions:
- The synergy of Shilnikov saddle-foci bifurcations is crucial for the global bifurcation unfolding in the Rössler model.
- Computational methods effectively reveal the mechanisms driving homoclinic chaos.
- The study provides insights into the complex interplay between bifurcations and chaotic attractors.
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