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Emergent oscillations in unidirectionally coupled overdamped bistable systems.
Adi R Bulsara1, Visarath In, Andy Kho
1Space and Naval Warfare Systems Center, Code 2363, 53560 Hull Street, San Diego, California 92152-5001, USA. bulsara@spawar.navy.mil
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
Summary
Dynamical systems that typically do not oscillate can be induced to do so through specific coupling. This controlled oscillation is useful for detecting weak target signals by analyzing changes in frequency and waveform asymmetry.
Area of Science:
- Physics
- Nonlinear Dynamics
- Ferromagnetism
Background:
- Overdamped unforced dynamical systems are known not to oscillate.
- Coupling schemes and initial conditions can induce oscillations in such systems above a control parameter threshold.
- Previous work demonstrated oscillation induction in a hysteretic ferromagnetic system.
Purpose of the Study:
- To explore the underlying dynamics of a system exhibiting induced oscillations.
- To derive scaling laws for oscillation frequency near the critical point.
- To analyze zero-crossing intervals in the presence of a target signal.
Main Methods:
- Analysis of a soft-potential mean-field model for a ferromagnetic sample.
- Investigation of N unidirectionally coupled elements with cyclic boundary conditions.
- Derivation of scaling laws and analysis of signal-induced dynamics.
Main Results:
- Oscillations are induced when coupling strength exceeds a critical value in the ferromagnetic system.
- Scaling laws governing oscillation frequency near the critical point were derived.
- Zero-crossing intervals were analyzed for symmetry-breaking target signals.
Conclusions:
- The induced oscillations offer a mechanism for detecting weak target signals.
- The derived scaling laws and interval analyses are crucial for signal detection and characterization.
- Understanding the system's dynamics enhances its application in sensitive signal detection.