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Route to hyperbolic hyperchaos in a nonautonomous time-delay system.
Pavel V Kuptsov1, Sergey P Kuznetsov2
1Laboratory of Topological Methods in Dynamics, National Research University Higher School of Economics, Nizhny Novgorod, 25/12 Bolshay Pecherskaya St., Nizhny Novgorod 603155, Russia.
Chaos (Woodbury, N.Y.)
|December 2, 2020
Summary
This study explores a self-oscillator with time delay, revealing a transition from non-hyperbolic to hyperbolic hyperchaos. The system exhibits chaotic dynamics, including intermittency and phase doubling, driven by nonlinear interactions.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Self-oscillators are fundamental in physics and engineering.
- Time delays introduce complex dynamics in dynamical systems.
- Nonlinearity is crucial for generating chaotic behavior.
Purpose of the Study:
- To investigate the transition from non-hyperbolic to hyperbolic hyperchaos in a time-delayed self-oscillator.
- To analyze the role of nonlinearity and phase doubling in driving chaotic dynamics.
- To characterize the different stages of the transition scenario.
Main Methods:
- Modeling a self-oscillator with a varied excitation parameter and time delay.
- Analyzing the system's dynamics using a chaotic Bernoulli-type map for phase evolution.
- Investigating the coupling strength and phase doubling intensity by varying delay time and excitation period.
Main Results:
- The system exhibits two coupled hyperbolic chaotic subsystems due to nonlinearity and time delay.
- A transition from non-hyperbolic to hyperbolic hyperchaos was observed.
- Four distinct stages of this transition were identified: intermittency, chaotic oscillations, plain hyperchaos, and hyperbolic hyperchaos.
Conclusions:
- Time-delayed self-oscillators can exhibit complex chaotic behaviors, including hyperchaos.
- The interplay between nonlinearity, time delay, and excitation parameters drives the transition to hyperbolic dynamics.
- Understanding these transitions is crucial for controlling and predicting the behavior of complex systems.
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