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Aging transition in mixed active and inactive fractional-order oscillators
Zhongkui Sun1, Yuanyuan Liu1, Ke Liu1
1Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China.
Chaos (Woodbury, N.Y.)
|November 3, 2019
Summary
This study explores aging transitions in fractional-order oscillators, finding that natural frequency and coupling strength significantly influence oscillation stability. A key discovery is the non-monotonic relationship between coupling strength and the critical ratio for aging transition.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Fractional calculus
Background:
- Aging transition is a critical phenomenon in coupled oscillators.
- Previous studies focused on integer-order systems.
- Fractional-order dynamics offer new avenues for research.
Purpose of the Study:
- Investigate aging transition in mixed active and inactive fractional-order oscillators.
- Analyze the impact of system parameters on aging transition.
- Explore novel phenomena in fractional-order Stuart-Landau oscillators.
Main Methods:
- Modeling coupled fractional-order Stuart-Landau oscillators.
- Analyzing the influence of distance parameter, coupling strength, and fractional-order derivative.
- Investigating the role of natural frequency and Hopf bifurcation.
Main Results:
- Heterogeneity arises from the distance parameter.
- Coupling strength and fractional-order derivative modulate the critical aging transition ratio.
- Increased natural frequency facilitates aging transition.
- Natural frequency can induce Hopf bifurcation, creating new heterogeneity.
- A non-monotonic dependence of the critical ratio on coupling strength was observed.
Conclusions:
- Fractional-order dynamics introduce unique behaviors in coupled oscillators.
- The robustness of oscillation is weakest at specific coupling strengths.
- This work expands understanding of aging transitions in complex systems.
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