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Tuning coupling rate to control oscillation quenching in fractional-order coupled oscillators
Shutong Liu1, Zhongkui Sun1, Nannan Zhao1
1Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China.
Chaos (Woodbury, N.Y.)
|November 3, 2020
Summary
Fractional-order derivatives enhance oscillation quenching in coupled dynamical systems. Introducing these derivatives can enlarge oscillation death ranges and induce quenching where it wouldn't otherwise occur.
Area of Science:
- Nonlinear dynamics
- Fractional calculus
- Complex systems
Background:
- Coupled dynamical systems exhibit complex behaviors.
- Fractional-order derivatives offer novel ways to model system dynamics.
- Oscillation quenching is a critical phenomenon in nonlinear systems.
Purpose of the Study:
- To compare the effects of fractional-order and integer-order derivatives on coupled oscillators.
- To analyze how fractional-order derivatives influence oscillation quenching.
- To investigate the transition from fake amplitude death to oscillation death.
Main Methods:
- Utilizing Stuart-Landau and Van der Pol oscillators as model systems.
- Tuning the coupling rate to transition between scalar and non-scalar coupling.
- Analyzing the onset and range of oscillation quenching behaviors.
Main Results:
- Fractional-order derivatives enlarge the range of oscillation death in coupled Stuart-Landau oscillators.
- A transition from fake amplitude death to oscillation death is observed with fractional-order derivatives.
- Oscillation quenching occurs in coupled Van der Pol systems exclusively with fractional-order derivatives.
Conclusions:
- Fractional-order derivatives play a significant role in controlling oscillation quenching.
- The findings provide insights into the mechanism of oscillation quenching in nonlinear models.
- This research highlights the importance of fractional-order dynamics in coupled systems.
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