Dynamics and Pattern Formation in Large Systems of Spatially-Coupled Oscillators with Finite Response Times
arXiv:1103.0323 · doi:10.1063/1.3596697
Abstract
We consider systems of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from other oscillators in its neighborhood. Using the ansatz of Ott and Antonsen (Ref. \cite{OA1}) and adopting a strategy similar to that employed in the recent work of Laing (Ref. \cite{Laing2}), we reduce the microscopic dynamics of these systems to a macroscopic partial-differential-equation description. Using this macroscopic formulation, we numerically find that finite oscillator response time leads to interesting spatio-temporal dynamical behaviors including propagating fronts, spots, target patterns, chimerae, spiral waves, etc., and we study interactions and evolutionary behaviors of these spatio-temporal patterns.
References in corpus (17)
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
- Partially integrable dynamics of hierarchical populations of coupled oscillators
- Solvable Model of Spiral Wave Chimeras
- Clustered chimera states in delay coupled oscillator systems
- Chimera states in heterogeneous networks
- Stability diagram for the forced Kuramoto model
- Self-Emerging and Turbulent Chimeras in Oscillator Chains
- Existence of hysteresis in the Kuramoto model with bimodal frequency distributions
- Bistable Chimera Attractors on a Triangular Network of Oscillator Populations
- Chimeras in a Network of Three Oscillator Populations with Varying Network Topology
- Noise-Induced Synchronization of a Large Population of Globally Coupled Nonidentical Oscillators
- Invariant submanifold for series arrays of Josephson junctions
- Phase resetting of collective rhythm in ensembles of oscillators
- Non-universal results induced by diversity distribution in coupled excitable systems
- Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case
- Low Dimensional Description of Pedestrian-Induced Oscillation of the Millennium Bridge
Cited by in corpus (18)
- The Kuramoto model in complex networks
- Chimera states: The Existence Criteria Revisited
- Transition from spatial coherence to incoherence in coupled chaotic systems
- Amplitude mediated chimera states
- Cluster Synchrony in Systems of Coupled Phase Oscillators with Higher-Order Coupling
- Cascades of Multi-headed Chimera States for Coupled Phase Oscillators
- Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths
- Hierarchical Synchrony of Phase Oscillators in Modular Networks
- Glassy states and superrelaxation in populations of coupled phase oscillators
- Collective modes of coupled phase oscillators with delayed coupling
- Complex macroscopic behavior in systems of phase oscillators with adaptive coupling
- Collective phase dynamics of globally coupled oscillators: Noise-induced anti-phase synchronization
- From the Kuramoto-Sakaguchi model to the Kuramoto-Sivashinsky equation
- Tiered synchronization in coupled oscillator populations with interaction delays and higher-order interactions
- Stability Diagram, Hysteresis, and Critical Time Delay and Frequency for the Kuramoto Model with Heterogeneous Interaction Delays
- Nonlinear transient waves in coupled phase oscillators with inertia
- Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state
- Competitive Suppression of Synchronization and Non-Monotonic Transitions in Oscillator Communities with Distributed Time Delay