Simplification of Stochastic Chemical Reaction Models with Fast and Slow Dynamics

Fokker-Planck analysis of stochastic coherence in models of an excitable neuron with noise in both fast and slow dynamics.

We provide a detailed and quantitative Fokker-Planck analysis of noise-induced periodicity (stochastic coherence, also known as coherence resonance) in both a discrete-time model and a continuous-time model of excitable neurons. In particular, we show that one-dimensional models can explain why the effects of noise added to the fast and slow dynamics of the models are dramatically different. We...

Slow manifold and averaging for slow-fast stochastic differential system

We consider multiscale stochastic dynamical systems. In this article an intermediate reduced model is obtained for a slow-fast system with fast mode driven by white noise. First, the reduced stochastic system on exponentially attracting slow manifold reduced system is derived to errors of O(ǫ). Second, averaging derives an autonomous deterministic system up to errors of O(√ǫ). Then an intermedi...

Fast and slow dynamics of the cytoskeleton.

Material moduli of the cytoskeleton (CSK) influence a wide range of cell functions. There is substantial evidence from reconstituted F-actin gels that a regime exists in which the moduli scale with frequency with a universal exponent of 3/4. Such behaviour is entropic in origin and is attributable to fluctuations in semiflexible polymers driven by thermal forces, but it is not obvious a priori ...

Stochastic dynamics on slow manifolds

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable simplification. In this article we demonstrate how the same basic methodology may also be applied to stochastic dynamical systems, by examining the behaviour...

Slow-fast Dynamics in Wonderland