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Symmetry breaking dynamics induced by mean-field density and low-pass filter
K Ponrasu1, Uday Singh2, K Sathiyadevi2
1Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur 613401, Tamil Nadu, India.
Chaos (Woodbury, N.Y.)
|June 4, 2020
Summary
Spontaneous symmetry breaking in coupled oscillators can lead to asymmetric states coexisting with amplitude death. The interplay of low-pass filters and mean-field density influences these complex dynamics.
Area of Science:
- Nonlinear Dynamics
- Complex Systems
- Theoretical Physics
Background:
- Spontaneous symmetry breaking (SSB) drives diverse dynamical states in coupled systems.
- SSB in coupled oscillators causes amplitude and phase variations.
- The influence of low-pass filters and mean-field parameters on SSB is not fully understood.
Purpose of the Study:
- To investigate the competing effects of low-pass filtering and mean-field density on symmetry breaking in coupled Stuart-Landau oscillators.
- To explore the emergence and coexistence of different dynamical states.
Main Methods:
- Analysis of conjugately coupled Stuart-Landau oscillators.
- Bifurcation analysis to examine dynamical transitions.
- Basin of attraction analysis to understand multi-stability.
Main Results:
- Emergence of a spontaneous symmetry breaking (asymmetric) oscillatory state coexisting with amplitude death.
- Asymmetric initial conditions favor SSB dynamics; symmetric conditions lead to amplitude death.
- The cut-off frequency of the low-pass filter and mean-field density jointly induce and enhance SSB.
Conclusions:
- The interaction between low-pass filtering and mean-field density is crucial for inducing and enhancing symmetry breaking dynamics.
- Initial state distribution significantly impacts the resulting dynamical state (SSB vs. amplitude death).
- Analytical stability curves for amplitude death and oscillation death states were derived.
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