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Low-dimensional dynamics of phase oscillators driven by Cauchy noise
1Graduate School of Data Science, Shiga University, 1-1-1 Banba, Hikone, Shiga 522-8522, Japan.
Physical Review. E
|November 20, 2020
Summary
Phase oscillator systems driven by Cauchy noise show low-dimensional dynamics. This finding simplifies studying identical or heterogeneous oscillators with or without noise.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics
Background:
- Phase oscillator systems with global sine coupling typically exhibit low-dimensional dynamics.
- Understanding noise-driven oscillator dynamics is crucial in various scientific fields.
Purpose of the Study:
- To extend the concept of low-dimensional dynamics to phase oscillator systems driven by Cauchy noise.
- To investigate the relationship between identical and heterogeneous oscillators under Cauchy noise influence.
Main Methods:
- Theoretical analysis of phase oscillator systems with global sine coupling and Cauchy noise.
- Numerical simulations of noise-driven phase oscillators.
Main Results:
- The study confirms low-dimensional dynamics in phase oscillator systems driven by Cauchy noise.
- Theoretical solutions for low-dimensional dynamics show strong agreement with numerical simulations.
- Identical oscillators with Cauchy noise exhibit dynamics similar to heterogeneous oscillators with Cauchy-distributed natural frequencies.
Conclusions:
- Low-dimensional dynamics can be effectively studied in phase oscillator systems with Cauchy noise.
- The findings enable the study of noise-driven identical oscillators via heterogeneous systems (without noise) and vice versa.
- This research offers a simplified approach to analyzing complex oscillator behaviors.
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