Optimal phase response curves for stochastic synchronization of limit-cycle oscillators by common Poisson noise

Abstract

We consider optimization of phase response curves for stochastic synchronization of non-interacting limit-cycle oscillators by common Poisson impulsive signals. The optimal functional shape for sufficiently weak signals is sinusoidal, but can differ for stronger signals. By solving the Euler-Lagrange equation associated with the minimization of the Lyapunov exponent characterizing synchronization efficiency, the optimal phase response curve is obtained. We show that the optimal shape mutates from a sinusoid to a sawtooth as the constraint on its squared amplitude is varied.

15 pages, 7 figures

References in corpus (4)

• Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
• The type II phase resetting curve is optimal for stochastic synchrony
• Synchronization of uncoupled oscillators by common gamma impulses: from phase locking to noise-induced synchronization
• Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

Cited by in corpus (6)

• Qualitative changes in spike-based neural coding and synchronization at the saddle-node loop bifurcation
• Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems
• Noise-induced synchronization of oscillatory convection and its optimization
• Criterion for noise-induced synchronization: application to colloidal alignment
• Design and control of noise-induced synchronization patterns
• How stochastic synchrony could work in cerebellar Purkinje cells