4 citations · 6 across the 5 of their papers we have counts for
5 papers
Instability of a nonlinear oscillator with small friction and small additive noise
Peter H Baxendale
Let denote the top Lyapunov exponent for the linearization along trajectories of the noisy damped non-linear oscillator ,…
Moment stability and large deviations for random dynamical systems on non-compact manifolds
Peter H Baxendale
The rate function for large deviations of the finite time Lyapunov exponent for the derived process in TM corresponding to a stochastic differential equation in M is related, via t…
Lyapunov exponents and shear-induced chaos for a Hopf bifurcation with additive noise
Peter H. Baxendale
This paper considers the effect of additive white noise on the normal form for the supercritical Hopf bifurcation in 2 dimensions. The main results involve the asymptotic behavior…
Noise Sharing and Mexican Hat Coupling in a Stochastic Neural Field
Peter H. Baxendale, Priscilla E. Greenwood, Lawrence M. Ward
A diffusion-type coupling operator biologically significant in neuroscience is a difference of Gaussian functions (Mexican Hat operator) used as a spatial-convolution kernel. We ar…
A Spectral Analysis of the Sequence of Firing Phases in Stochastic Integrate-and-Fire Oscillators
Peter Baxendale, John Mayberry
Integrate and fire oscillators are widely used to model the generation of action potentials in neurons. In this paper, we discuss small noise asymptotic results for a class of stoc…