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Amplitude death in time-delay nonlinear oscillators coupled by diffusive connections.
Keiji Konishi1, Katsuhisa Senda, Hideki Kokame
1Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka, 599-8531 Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2008
Summary
Static connections do not cause amplitude death in time-delay oscillators. Dynamic and delayed connections can prevent amplitude death, with conditions for this instability identified and experimentally verified. This research advances understanding of coupled nonlinear oscillators.
Area of Science:
- Nonlinear Dynamics
- Control Theory
- Systems Engineering
Background:
- Amplitude death is a phenomenon in coupled oscillators where oscillations cease.
- Time-delay systems introduce complexity in stability analysis.
- Understanding coupling mechanisms is crucial for controlling oscillator behavior.
Purpose of the Study:
- Analyze the stability of amplitude death in time-delay nonlinear oscillators.
- Investigate the role of static, dynamic, and delayed coupling.
- Provide methods for predicting and controlling amplitude death.
Main Methods:
- Mathematical stability analysis of coupled scalar time-delay nonlinear oscillators.
- Derivation of instability conditions for dynamic and delayed connections.
- Development of a procedure for estimating amplitude death region boundaries.
- Experimental verification using electronic circuits.
Main Results:
- Static connections were found to never induce amplitude death.
- A simple instability condition was derived for dynamic and delayed connections, preventing death.
- A systematic method for estimating the boundaries of amplitude death regions was established.
- Analytical findings were confirmed through electronic circuit experiments.
Conclusions:
- The type of coupling significantly influences the occurrence of amplitude death.
- Time-delay oscillators with static connections are robust against amplitude death.
- Conditions for preventing amplitude death in systems with dynamic/delayed coupling were identified.
- The study provides a framework for analyzing and controlling amplitude death in complex oscillator networks.
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