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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.
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Ermentrout et al. (1980) studied this question.
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