Symmetry and phase-locking in a ring of pulse-coupled oscillators with distributed delays

DOI10.1016/S0167-2789(98)00264-4zbMath0937.34060MaRDI QIDQ1808254

Stephen Coombes, Paul C. Bressloff

Publication date: 6 December 1999

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

stabilityoscillationbifurcationphase-lockingsymmetry breakingdistributed delayspulse-coupled integrate-and-fire oscillatorstravelling wave state

Mathematics Subject Classification ID

Stability theory of functional-differential equations (34K20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Periodic solutions to functional-differential equations (34K13)

Related Items

Mathematical frameworks for oscillatory network dynamics in neuroscience, Unsupervised learning of arbitrarily shaped clusters using ensembles of Gaussian models, Network architecture and spatio-temporally symmetric dynamics, Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks, A mathematical model of motorneuron dynamics in the heartbeat of the leech, Phase models and clustering in networks of oscillators with delayed coupling, Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks, Linearized oscillation theory for a nonlinear equation with a distributed delay, Analysis of pulse period for passive neuron in pulse coupled neural network, Phase locking in networks of synaptically coupled McKean relaxation oscillators, Synchrony, stability, and firing patterns in pulse-coupled oscillators, Travelling waves in chains of pulse-coupled integrate-and-fire oscillators with distributed delays, Dynamics of traveling pulses developed in a tunnel diode oscillator ring for multiphase oscillation, Bifurcation analysis of a class of first-order nonlinear delay-differential equations with reflectional symmetry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Chemical oscillations, waves, and turbulence
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The behavior of rings of coupled oscillators
• Bifurcation of periodic motions in two weakly coupled van der Pol oscillators
• Averaging of globally coupled oscillators
• Singularities and groups in bifurcation theory. Volume II
• Coupled nonlinear oscillators and the symmetries of animal gaits
• Constants of motion for superconducting Josephson arrays
• Weakly connected neural networks
• The dynamics of \(n\) weakly coupled identical oscillators
• The role of axonal delay in the synchronization of networks of coupled cortical oscillators
• Multiple pulse interactions and averaging in systems of coupled neural oscillators
• Synchronization of Pulse-Coupled Biological Oscillators
• Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I.
• Three identical oscillators with symmetric coupling
• Symmetric chaos in systems of three and four forced oscillators
• Phase Transitions and Other Phenomena in Chains of Coupled Oscillators
• Symmetry and phaselocking in chains of weakly coupled oscillators
• Patterns at Primary Hopf Bifurcations of a Plexus of Identical Oscillators
• Coupled arrays of Josephson junctions and bifurcation of maps with S_Nsymmetry
• Oscillator Death in Systems of Coupled Neural Oscillators
• Self-organized criticality in a cellular automaton model of pulse-coupled integrate-and-fire neurons
• BIFURCATIONS IN HEART RHYTHMS
• STABILITY OF SYNCHRONIZATION IN NETWORKS OF DIGITAL PHASE-LOCKED LOOPS
• Integrability of a globally coupled oscillator array
• The chemical basis of morphogenesis
• Integrate-and-Fire Models of Nerve Membrane Response to Oscillatory Input