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Supertransient Chaos in a Single and Coupled Liénard Systems.
S Leo Kingston1, Suresh Kumarasamy2, Agnieszka Chudzik1
1Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland.
We observed supertransient chaos in Liénard systems, featuring extremely long transient dynamics before settling into periodic behavior. This phenomenon, including hyperchaos, was studied in coupled systems with external forcing.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Electronic Circuits
Background:
- Liénard systems are fundamental in nonlinear dynamics.
- Transient chaos describes systems with long-lived chaotic behavior before reaching a steady state.
- External periodic forcing can significantly alter system dynamics.
Purpose of the Study:
- To investigate supertransient chaos in single and coupled Liénard systems.
- To analyze the impact of external periodic force on transient dynamics.
- To explore conditions leading to supertransient hyperchaotic dynamics.
Main Methods:
- Numerical simulations of Liénard systems.
- Analysis of transient dynamics and steady states.
- Statistical analysis and hardware implementation using analog circuits.
Main Results:
- Supertransient chaos was observed in single and coupled Liénard systems.
- Coupled systems exhibited extremely long transient dynamics with mismatched forcing frequencies.
- Supertransient hyperchaotic dynamics were identified for specific parameter sets.
Conclusions:
- External periodic forcing can induce and prolong chaotic transient dynamics in Liénard systems.
- Coupled Liénard systems offer a platform for observing complex transient phenomena like supertransient hyperchaos.
- The findings were validated through numerical, statistical, and experimental methods.
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