Stability of splay states in globally coupled rotators

Abstract

The stability of dynamical states characterized by a uniform firing rate ({\it splay states}) is analyzed in a network of $N$ globally pulse-coupled rotators (neurons) subject to a generic velocity field. In particular, we analyse short-wavelength modes that were known to be marginally stable in the infinite $N$ limit and show that the corresponding Floquet exponent scale as $1/N^2$. Moreover, we find that the sign, and thereby the stability, of this spectral component is determined by the sign of the average derivative of the velocity field. For leaky-integrate-and-fire neurons, an analytic expression for the whole spectrum is obtained. In the intermediate case of continuous velocity fields, the Floquet exponents scale faster than $1/N^2$ (namely, as $1/N^4$) and we even find strictly neutral directions in a wider class than the sinusoidal velocity fields considered by Watanabe and Strogatz in {\it Physica D 74 (1994) 197-253}.

arXiv comment7.7 pages - 16 Figures - Submitted to Physical Review E

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Cited by in corpus (9)

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• Heterogeneous Mean Field for neural networks with short term plasticity
• Splay states in finite pulse-coupled networks of excitable neurons
• Linear stability in networks of pulse-coupled neurons
• Neural networks with excitatory and inhibitory components: direct and inverse problems by a mean-field approach