Noise-induced pattern formation in excitable media [article]

Valentina Beato, Harald Engel, Technische Universität Berlin, Technische Universität Berlin
2007
In the present work we study spontaneous formation of spatio-temporal patterns in excitable media, where external fluctuations with spatial and temporal correlation are present. We firstly restrict us to single excitable elements without spatial coupling and thereby we analyse numerically two different excitable models: the FitzHugh-Nagumo model for the action potential variations in a neuron, and the Oregonator model for the light-sensitive Belousov-Zhabotinsky reaction. In both models
more » ... both models external fluctuations are taken into account in the excitability parameter. We show that beside the noise intensity, also the correlation time is able to control the coherence of the system response to noise. An excitable element is brought from an highly incoherent regime to a coherent one by an appropriate choice of the correlation time. This effect has been found both in the FitzHugh-Nagumo model driven by an Ornstein-Uhlenbeck process and in the Oregonator model driven by a dichotomous telegraph signal. In the latter case we are able to connect the optimal correlation time, for which the system behaviour is most coherent, with a characteristic time scale of the system. We develop an experimental set-up to study the coherence of noise induced activity in the light-sensitive Belousov-Zhabotinsky reaction. By tracking the noise induced nucleations we are able to analyse the coherence properties of the reaction under fluctuating light intensity. The experimental measures accurately reproduce what found with simulations in the Oregonator model. We introduce spatial diffusive coupling in the Oregonator model and we study the statio-temporal patterns induced under conditions of fluctuating excitability. Here both spatial and temporal correlations have been considered. We find that also the tuning of the correlation length allows to enhance the coherence of the system behaviour. Choosing both correlation time and length appropriately highly spatially and temporally coherent patterns emerge in the excitable medium. Furthermore, we are [...]
doi:10.14279/depositonce-1519 fatcat:cmzfjt4xird5dmrggyirjn73zi