Lyapounov exponent of linear stochastic systems with large diffusion term

AbstractWe study the behaviour of the Lyapounov exponent of the solution of dXtAXt+δ∑i1rBkXt∘dWkt, as σ→∞. We obtain the exact behaviour in two cases for arbitrary dimensions, and in most cases for the two dimensional equation

The type II phase resetting curve is optimal for stochastic synchrony

The phase-resetting curve (PRC) describes the response of a neural oscillator to small perturbations in membrane potential. Its usefulness for predicting the dynamics of weakly coupled deterministic networks has been well characterized. However, the inputs to real neurons may often be more accurately described as barrages of synaptic noise. Effective connectivity between cells may thus arise in the form of correlations between the noisy input streams. We use constrained optimization and perturbation methods to prove that PRC shape determines susceptibility to synchrony among otherwise uncoupled noise-driven neural oscillators. PRCs can be placed into two general categories: Type I PRCs are non-negative while Type II PRCs have a large negative region. Here we show that oscillators with Type II PRCs receiving common noisy input sychronize more readily than those with Type I PRCs.Comment: 10 pages, 4 figures, submitted to Physical Review

Nonlinear oscillator with parametric colored noise: some analytical results

The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as compared to the energy. Thus, an effective stochastic dynamics for the energy can be derived if the angular variable is averaged out. However, the standard elimination procedure, performed earlier for a Gaussian white noise, fails when the noise is colored because of correlations between the noise and the fast angular variable. We develop here a specific averaging scheme that retains these correlations. This allows us to calculate the probability distribution function (P.D.F.) of the system and to derive the behavior of physical observables in the long time limit

Lyapounov exponent of linear stochastic systems with large diffusion term

We study the behaviour of the Lyapounov exponent of the solution of , as [sigma]-->[infinity]. We obtain the exact behaviour in two cases for arbitrary dimensions, and in most cases for the two dimensional equation.

Lyapunov exponent and rotation number of two dimensional linear stochastic systems with small diffusion

SIGLETIB: RA 6154 (151) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Representation, positivity and expansion of Lyapunov exponents for linear stochastic systems

SIGLETIB: RA 6154 (127) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications

SIGLETIB: RA 6154 (134) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman