Stability of splay states in globally coupled rotators

Details Stability of splay states in globally coupled rotators Stability of splay states in globally coupled rotators

2009-03-10

arxiv.org/abs/0903.1867v2

Phys. Rev. E 80, 036209 (2009)

Physics

Condensed Matter

Disordered Systems and Neural Networks

7.7 pages - 16 Figures - Submitted to Physical Review E

Scientific paper

10.1103/PhysRevE.80.036209

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}.

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