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Stability and dynamics of nonautonomous systems with pulsed nonlinearity
Yannis Kominis1, Tassos Bountis
1School of Electrical and Computer Engineering, National Technical University of Athens, Zographou GR-15773, Greece and Department of Mathematics, University of Patras, Patras GR-26500, Greece.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 16, 2013
Summary
Control over nonautonomous systems with pulsed nonlinearity is achieved by adjusting parameters. This allows for stable localized excitations in coupled oscillators, enabling controlled dynamics.
Area of Science:
- Nonlinear dynamics
- Control theory
- Complex systems
Background:
- Nonautonomous systems exhibit complex behaviors.
- Pulsed nonlinearities introduce unique dynamical properties.
- Understanding control mechanisms is crucial for applications.
Purpose of the Study:
- Investigate control capabilities in nonautonomous systems with pulsed nonlinearity.
- Analyze how parameter selection alters fundamental dynamical properties.
- Explore the stabilization of localized excitations in coupled systems.
Main Methods:
- Analysis of single oscillators under periodic linear and nonlinear intervals.
- Study of coupled oscillator chains with pulsed onsite nonlinearity.
- Parameter variation to assess stability and phase space topology.
Main Results:
- Single oscillator stability and phase space topology depend on oscillation frequency and interval durations.
- Parameter selection can stabilize unstable zero background in coupled oscillators.
- Dynamically robust localized excitations can be created and controlled.
Conclusions:
- Parameter tuning offers significant control over pulsed nonlinear systems.
- Stabilization of localized excitations is achievable through appropriate parameter choices.
- Explicit determination and control of excitation evolution properties are possible.
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