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We examine the ability of intrinsic noise to produce complex temporal dynamics in Turing pattern formation systems, with particular emphasis on the Schnakenberg kinetics. Using power spectral methods, we characterize the behavior of the system using stochastic simulations at a wide range of points in parameter space and compare with analytical approximations. Specifically, we investigate whether polarity switching of stochastic patterns occurs at a defined frequency. We find that it can do so in individual realizations of a stochastic simulation, but that the frequency is not defined consistently across realizations in our samples of parameter space. Further, we examine the effect of noise on deterministically predicted traveling waves and find them increased in amplitude and decreased in speed.

Original publication

DOI

10.1103/PhysRevE.87.042719

Type

Journal article

Journal

Phys Rev E Stat Nonlin Soft Matter Phys

Publication Date

04/2013

Volume

87

Keywords

Diffusion, Kinetics, Nonlinear Dynamics, Spatio-Temporal Analysis, Stochastic Processes