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On discrete Lorenz-like attractors
Sergey Gonchenko1, Alexander Gonchenko1, Alexey Kazakov2
1Mathematical Center of Lobachevsky State University, 23 Prospekt Gagarina, 603950 Nizhny Novgorod, Russia.
Chaos (Woodbury, N.Y.)
|March 3, 2021
Summary
This study explores chaotic discrete Lorenz-like attractors, revealing universal bifurcation scenarios that generate them. These scenarios can lead to new types of Lorenz attractors through period-2 attractors and crises.
Area of Science:
- Dynamical Systems
- Chaos Theory
- Nonlinear Dynamics
Background:
- Discrete Lorenz-like attractors exhibit complex dynamical behaviors.
- Understanding their formation is crucial for nonlinear dynamics.
Purpose of the Study:
- Investigate geometrical and dynamical properties of discrete Lorenz-like attractors.
- Describe universal bifurcation scenarios leading to these attractors.
- Analyze the emergence of new attractor types through crises.
Main Methods:
- Phenomenological description of bifurcation scenarios.
- Demonstration using one-parameter families of 3D Hénon-like maps.
- Analysis of period-2 Lorenz-like attractors and their crises.
Main Results:
- Robustly chaotic (pseudohyperbolic) attractors arise from universal bifurcation scenarios.
- Specific scenarios leading to period-2 Lorenz-like attractors are identified.
- Crises of period-2 attractors generate novel discrete Lorenz shape attractors.
Conclusions:
- Universal bifurcations provide a framework for understanding discrete Lorenz-like attractor formation.
- Period-2 attractors and their crises are key mechanisms for generating complex dynamics.
- The study expands the known types of discrete Lorenz attractors.
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