We consider the existence and stability of multibump solutions of a class of integral-differential equations modeling a single layer of homogeneous neural network with both excitatory and inhibitory neurons. The existence results are obtained by combining several shifts of a one-bump solution. Dynamical properties are obtained by considering the equation as an infinite-dimensional dynamical system and the spectrum of multibump solutions in terms of the weight functions. The center manifold theory and its foliation are used to show exponential stability with asymptotic phase for multibump solutions. Numerical results for some possible bifurcation phenomena are also presented.
Relation:
International Journal of Bifurcation and Chaos 17(11), pp.4099-4115
