Effect of noise and perturbations on limit cycle systems (Q1179047)

The paper is focused on biological systems and on corresponding models that exhibit excitable or oscillatory behaviour, mainly on the dynamics of a single neuron. The authors show that the influence of noise and of external perturbations on a nonlinear oscillator can vary strongly along a limit cycle and upon transition from limit cycle to stationary behaviour. The proofs are based on the van Kampen approximation for solutions of the Fokker-Planck equation in the limit of weak noise. The key result is that noise induces diffusion-like spread along the limit cycle, but quasistationary behaviour normal to the limit cycle.