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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Qualitative Analysis and Bifurcation in a Neuron System With Memristor Characteristics and Time Delay
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Qualitative Analysis and Bifurcation in a Neuron System With Memristor Characteristics and Time Delay

机译：具有忆阻特性和时间延迟的神经元系统中的定性分析与分叉

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摘要

This article focuses on the hybrid effects of memristor characteristics, time delay, and biochemical parameters on neural networks. First, we propose a novel neuron system with memristor and time delays in which the memristor is characterized by a smooth continuous cubic function. Second, the existence of equilibria of this type of neuron system is examined in the parameter space. Sufficient conditions that ensure the stability of equilibria and occurrence of pitchfork bifurcation are given for the memristor-based neuron system without delay. Third, some novel criteria of the addressed neuron system are constructed for guaranteeing the delay-dependent and delay-independent stability. The specific conditions are provided for Hopf bifurcations, and the properties of Hopf bifurcation are ascertained using the center manifold reduction and the normal form theory. Moreover, there exists a phenomenon of bistability for the delayed memristor-based neuron system having three equilibria. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.
机译：本文重点介绍了神经网络上的映像特性，时间延迟和生物化学参数的混合效应。首先，我们提出了一种具有忆阻器和时间延迟的新型神经元系统，其中存储器的特征在于光滑连续立方函数。其次，在参数空间中检查了这种类型神经元系统的均衡的存在。确保均衡稳定性的充分条件和干燥物沸腾分叉的发生的稳定性是基于忆耳的神经元系统，没有延迟。第三，构建了寻址神经元系统的一些新的标准，用于保证延迟依赖性和延迟无关的稳定性。对于Hopf分叉提供的具体条件，利用中心歧管减少和正常形式理论确定Hopf分叉分叉的性质。此外，存在具有三个平衡的基于延迟映射器的神经元系统的双稳态的现象。最后，通过数值例子证明了理论结果的有效性。

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