Stability of splay states in globally coupled rotators.
The stability of dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of N globally pulse-coupled rotators (neurons) subject to a generic velocity field. In particular, we analyze 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/N2. 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/N2 (namely, as 1/N4) and we even find strictly neutral directions in a wider class than the sinusoidal velocity fields considered by Watanabe and Strogatz [Physica D 74, 197 (1994)].
Calamai
Massimo
M
Istituto dei Sistemi Complessi, CNR, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy. massimo.calamai@gmail.com
Politi
Antonio
A
Torcini
Alessandro
A
D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009991:Oscillometry / Q000379:methods*