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Nonconventional synchronization and energy localization in weakly coupled autogenerators
Margarita Kovaleva1, Valery Pilipchuk2, Leonid Manevitch1
1N.N. Semenov Institute of Chemical Physics, Kosygin St., 4 Moscow 119991, Russia.
Physical Review. E
|October 15, 2016
Summary
This study reveals non-stationary synchronization in coupled oscillators, characterized by intense energy exchange. Parameter changes alter dynamics, linking stationary and non-stationary states to distinct nonlinear modes.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Oscillator theory
Background:
- Previous work identified a novel synchronization type in coupled van der Pol-Duffing autogenerators.
- This synchronization involves significant energy exchange between oscillators, deviating from stationary behavior.
Purpose of the Study:
- To investigate the influence of frequency detuning on non-stationary synchronization dynamics.
- To analyze how nonlinearity and dissipation affect energy exchange patterns in coupled oscillators.
Main Methods:
- Utilized a generalized model of two weakly coupled van der Pol-Duffing autogenerators.
- Employed phase plane diagrams and limiting phase trajectories to analyze dynamics.
- Examined the effects of varying frequency detuning, nonlinearity, and dissipation parameters.
Main Results:
- Frequency detuning, nonlinearity, and dissipation significantly alter phase diagrams of energy exchange.
- Transitions observed from intensive energy exchange to localized exchange on a single oscillator.
- Non-stationary synchronization dynamics were characterized by constant phase shifts with brief transitional intervals.
Conclusions:
- Stationary synchronization corresponds to nonlinear normal modes.
- Non-stationary synchronization is associated with local modes and involves intensive energy exchange.
- Limiting phase trajectories play a crucial role in understanding non-stationary synchronization, analogous to nonlinear normal modes in stationary states.
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