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Shearless and periodic attractors in the dissipative Labyrinthic map.
L F B Souza1, R Egydio de Carvalho2, R L Viana3
1Institute of Physics, University of São Paulo, São Paulo 13506-900, SP, Brazil.
Chaos (Woodbury, N.Y.)
|December 5, 2024
Summary
This study explores a dissipative Labyrinthic map, revealing how dissipation impacts the shearless curve and creates chaotic attractors. It introduces the Curry-Yorke route to chaos and uses basin entropy to analyze system multi-stability.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Statistical mechanics
Background:
- The Labyrinthic map, a 2D area-preserving system, possesses a shearless curve acting as a transport barrier.
- Dissipative systems introduce energy loss, potentially altering the dynamics of conservative systems.
Purpose of the Study:
- To investigate the effect of dissipation on the shearless curve in the Labyrinthic map.
- To characterize the emergence of quasi-periodic and chaotic attractors (shearless attractors).
- To analyze system multi-stability and explore routes to chaos.
Main Methods:
- Numerical investigation of a dissipative Labyrinthic map.
- Application of basin entropy and boundary basin entropy for multi-stability analysis.
- Identification of the Curry-Yorke route to chaos.
Main Results:
- Dissipation modifies the shearless curve, leading to the formation of shearless attractors.
- The Curry-Yorke route to chaos was identified for the shearless attractor.
- Basin entropy analysis revealed diverse multi-stability scenarios.
Conclusions:
- Dissipation fundamentally alters the dynamics of the Labyrinthic map, transforming its transport barrier properties.
- The study provides insights into routes to chaos and multi-stability in dissipative dynamical systems.
- Numerical methods effectively characterize complex dynamics and emergent structures.
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