具有奇异脉冲的Wilson-Cowan模型的分岔分析
Bifurcation analysis of Wilson-Cowan model with singular impulses
摘要：
研究了具有脉冲的Wilson-Cowan神经网络模型。研究的主要新颖之处在于，除了传统的奇异性模型，我们考虑奇异脉冲。提出了一种新的分析方法。这允许考虑模型的解的存在性，并且通过数值模拟观察到最终神经行为的分叉。分岔是由模型中的脉冲和奇异性引起的，它们涉及吸引子的结构，吸引子由相空间中新引入的集合组成，如水母和环。
英文摘要：
The paper concerns with Wilson-Cowan neural model with impulses. The main novelty of the study is that besides the traditional singularity of the model, we consider singular impulses. A new technique of analysis of the phenomenon is suggested. This allows to consider the existence of solutions of the model and bifurcation in ultimate neural behavior is observed through numerical simulations. The bifurcations are reasoned by impulses and singularity in the model and they concern the structure of attractors, which consist of newly introduced sets in the phase space such that medusas and rings.
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