Chimera Dynamics of Generalized Kuramoto-Sakaguchi Oscillators in Two-population Networks
arXiv:2306.13616 · doi:10.1088/1751-8121/acf4d6
Abstract
Chimera dynamics is characterized by the coexistence of coherence and incoherence, arising from a symmetry-breaking mechanism. Extensive research has been performed in various systems, focusing on a system of Kuramoto-Sakaguchi (KS) phase oscillators. In recent developments, the system has been extended to the so-called generalized Kuramoto model, wherein an oscillator is situated on the surface of an M-dimensional unit sphere, rather than being confined to a unit circle. In this paper, we exploit the model introduced in New. J. Phys. 16, 023016 (2014) where the macroscopic dynamics of the system was studied using the extended Watanabe-Strogatz transformation both for real and complex spaces. Considering two-population networks of the generalized KS oscillators in 2D complex spaces, we demonstrate the existence of chimera states and elucidate different motions of the order parameter vectors depending on the strength of intra-population coupling. Similar to the KS model on the unit circle, stationary and breathing chimeras are observed for comparatively strong intra-population coupling. Here, the breathing chimera changes their motion upon decreasing intra-population coupling strength via a global bifurcation involving the completely incoherent state. Beyond that, the system exhibits periodic alternation of the two order parameters with weaker coupling strength. Moreover, we observe that the chimera state transitions into a componentwise aperiodic dynamics when the coupling strength weakens even further. The aperiodic chimera dynamics emerges due to the breaking of conserved quantities that are preserved in the stationary, breathing and alternating chimera states. We provide a detailed explanation of this scenario in both the thermodynamic limit and for finite-sized ensembles. Furthermore, we note that an ensemble in 4D real spaces demonstrates similar behavior.
References in corpus (35)
- Chimera States for Coupled Oscillators
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
- Solvable model for chimera states of coupled oscillators
- Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
- Long Time Evolution of Phase Oscillator Systems
- Partially integrable dynamics of hierarchical populations of coupled oscillators
- Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
- Synchronization of two interacting populations of oscillators
- Phase oscillators with global sinusoidal coupling evolve by Mobius group action
- Theory and computation of covariant Lyapunov vectors
- Low-dimensional dynamics of populations of pulse-coupled oscillators
- Chimeras in networks of planar oscillators
- Chimera states in networks of phase oscillators: the case of two small populations
- Intermittent chaotic chimeras for coupled rotators
- Continuous versus Discontinuous Transitions in the -Dimensional Generalized Kuramoto Model: Odd is Different
- Bistable Chimera Attractors on a Triangular Network of Oscillator Populations
- Chimeras in a Network of Three Oscillator Populations with Varying Network Topology
- Covariant Lyapunov vectors
- Chimera states in coupled Kuramoto oscillators with inertia
- Chimera states in two populations with heterogeneous phase-lag
- Chaotic Weak Chimeras and their Persistence in Coupled Populations of Phase Oscillators
- Heteroclinic switching between chimeras
- Solvable model of the collective motion of heterogeneous particles interacting on a sphere
- Complexity Reduction Ansatz for Systems of Interacting Orientable Agents: Beyond The Kuramoto Model
- Solvable Dynamics of Coupled High-Dimensional Generalized Limit-Cycle Oscillators
- Multi-Population Phase Oscillator Networks with Higher-Order Interactions
- Complexity reduction in the 3D Kuramoto model
- Ott-Antonsen ansatz for the D-dimensional Kuramoto model: a constructive approach
- Heteroclinic Dynamics of Localized Frequency Synchrony: Heteroclinic Cycles for Small Populations
- Generalized frustration in the multidimensional Kuramoto model
- Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators
- On synchronization in Kuramoto models on spheres
- Heteroclinic Switching between Chimeras in a Ring of Six Oscillator Populations
- Chaotic Chimera Attractors in a Triangular Network of Identical Oscillators