In this paper, a neutral functional differential equation with multiple delays is considered. In a first step, we assumed some sufficient hypotheses to guarantee the existence of the Bogdanov–Takens and the triple-zero bifurcations. In a second step, the normal form of the two bifurcations is obtained by using the reduction on the center manifold and the theory of the normal form. Finally, we applied our study to a class of three-neuron bidirectional associative memory networks, its dynamic behaviors are studied and proved by an example and its numerical simulations.

中文翻译：

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具有多重时滞的中立型泛函微分方程的Bogdanov–Takens和三重零分叉

本文考虑了具有多个时滞的中立型泛函微分方程。第一步，我们假设了足够的假设来保证Bogdanov-Takens和三零分叉的存在。在第二步中，通过使用中心歧管上的约简和法线形式的理论来获得两个分叉的法线形式。最后，我们将研究成果应用于一类三神经元双向联想记忆网络，并通过实例和数值模拟对它的动态行为进行了研究和证明。