A mathematical criterion based on phase response curves for stability in a ring of coupled oscillators

摘要: Canavier et al. (1997) used phase response curves (PRCs) of individual oscillators to characterize the possible modes phase-locked entrainment an N-oscillator ring network. We extend this work by developing a mathematical criterion determine local stability such mode based on PRCs. Our method does not assume symmetry; neither nor their connections need be identical. To use these techniques for predicting and determining stability, one only PRC each oscillator in either experimentally or from computational model. show that network cannot determined simply testing ability entrain next. Stability depends number neurons ring, type mode, slope at point respective neuron. also describe simple criteria which are necessary sufficient examine implications results.