Noise induced complexity: From subthreshold oscillations to spiking in coupled excitable systems

• Published in: Chaos (Woodbury, N.Y.) N.Y.), 2005-06, Vol.15 (2), p.26117-26117
• Main Authors: Zaks, M. A., Sailer, X., Schimansky-Geier, L., Neiman, A. B.
• Format: Article
• Language: English
• Subjects: Action Potentials; Animals; Axons; Models, Neurological; Models, Theoretical; Nonlinear Dynamics; Normal Distribution; Oscillometry; Physics - methods; Stochastic Processes; Thermodynamics; Time Factors
• ISSN: 1054-1500; 1089-7682
• DOI: 10.1063/1.1886386

We study the stochastic dynamics of an ensemble of N globally coupled excitable elements. Each element is modeled by a FitzHugh–Nagumo oscillator and is disturbed by independent Gaussian noise. In simulations of the Langevin dynamics we characterize the collective behavior of the ensemble in terms of its mean field and show that with the increase of noise the mean field displays a transition from a steady equilibrium to global oscillations and then, for sufficiently large noise, back to another equilibrium. In the course of this transition diverse regimes of collective dynamics ranging from periodic subthreshold oscillations to large-amplitude oscillations and chaos are observed. In order to understand the details and mechanisms of these noise-induced dynamics we consider the thermodynamic limit N → ∞ of the ensemble, and derive the cumulant expansion describing temporal evolution of the mean field fluctuations. In Gaussian approximation this allows us to perform the bifurcation analysis; its results are in good qualitative agreement with dynamical scenarios observed in the stochastic simulations of large ensembles.