Liapunov functional for a delayed integro-differential equation model of a neural fieldM. Enculescu and M. Bestehorn
Lehrstuhl für Theoretische Physik II, Brandenburgische Technische Universität Cottbus - Erich-Weinert-Strasse 1, 03046 Cottbus, Germany
received 18 September 2006; accepted in final form 2 February 2007; published March 2007
published online 13 March 2007
We find a non-local energy functional for a scalar neural field with two stable steady states. The time evolution of the membrane potential of the network can be obtained from the gradient flow of this functional. It is shown that this approach can be used to energetically explain some of the properties of traveling wave fronts connecting the two stable states, such as the direction of the propagation velocity.
87.10.+e - General theory and mathematical aspects.
87.18.Sn - Neural networks.
05.45.-a - Nonlinear dynamics and chaos.
© Europhysics Letters Association 2007