Secondary Bifurcation in Neuronal Nets
G. Bard Ermentrout, Jack D. Cowan · SIAM Journal on Applied Mathematics · 1980
The possibility of multiple complex eigenvalues in a neural net is demonstrated. Group theoretic techniques are used to derive the bifurcation equations near multiple complex eigenvalues. A selection mechanism between standing and traveling waves is shown that depends only on internal parameters. Quasi-periodic solutions and hysteresis between different oscillations are obtained. The application of this model to the study of epileptic behavior is discussed.