Excitable systems under noise

Increasing noise in nonlinear systems far from equilibrium may induce a more ordered state compared with the case without noise. Our interest is devoted to excitable systems which model a wide class of dynamical behavior in biophysics and chemistry. We formulate a noisy FitzHugh-Nagumo dynamics and discuss the dynamic output by stochastic measures as the stationary spike generation rates, the spike diffusion coefficient and the power spectrum. The analysis shows that deterministic bistable and excitable dynamics converts into stochastic oscillating systems with a high value of the oscillations for non-vanishing noise.

As an application we investigate the temporal behaviour of a cluster of inositol-(1,4,5)-triphosphate receptor (IP3R)-I channels. We obtain the spectrum of the calcium signal within a cluster. We compare these results with stochastic simulations and obtain an intermediate number of channels per cluster for optimal signalling periodicity.

We also study a cluster of N globally coupled FitzHugh-Nagumo systems and find a rather complex sequence of transitions if noise induced oscillations are generated. These numeric findings were completed by a bifurcation analysis of the dynamics of relevant cumulants which qualitatively agrees well with the simulations.

Literature:
B. Lindner, J. Garcia-Ojalvo, A. Neiman, and L. Schimansky-Geier, Phys. Report 392, 321-424 (2004).
B. Lindner and L. Schimansky-Geier, Phys. Rev E 61, 6103-6110 (2000)
B. Lindner, L. Schimansky-Geier, and A. Longtin Phys. Rev. E 66, 031916 (2002).
L. Meinhold and L. Schimansky-Geier, Phys. Rev. E 66, 050901 (2002).
M. Zaks, X. Sailer, L. SChimansky-Geier, and A. Neiman, Noise Induced Complexity: From Sub- to Superthreshold Oscillations in Coupled Excitable Systems, submitted 2004.