将神经递质纳入模型，推导出稳定网络的数学条件。
Transmission Neural Networks: Inhibitory and Excitatory Connections
- 用连续状态建模神经元，统一处理兴奋与抑制连接
- 当突触神经递质数量趋于无穷时，建立极限网络模型
- 给出该模型稳定性和收缩性的充分条件，适合理论研究者
本文扩展了Gao和Caines提出的传输神经网络模型，引入抑制性连接和神经递质群体。新模型包含二值神经元状态、传输动态以及兴奋与抑制连接。在技术假设下，建立了神经元放电概率的表征，并证明该表征可等价地由每个神经元具有二维连续状态的神经网络实现。进一步，将神经递质群体纳入建模，并在所有突触连接上的神经递质数量趋于无穷时，建立了极限网络模型。最后，给出了该极限网络模型稳定性与收缩性质的充分条件。
原文摘要 · Abstract (English)
This paper extends the Transmission Neural Network model proposed by Gao and Caines in [1]-[3] to incorporate inhibitory connections and neurotransmitter populations. The extended network model contains binary neuronal states, transmission dynamics, and inhibitory and excitatory connections. Under technical assumptions, we establish the characterization of the firing probabilities of neurons, and show that such a characterization considering inhibitions can be equivalently represented by a neural network where each neuron has a continuous state of dimension 2. Moreover, we incorporated neurotransmitter populations into the modeling and establish the limit network model when the number of neurotransmitters at all synaptic connections go to infinity. Finally, sufficient conditions for stability and contraction properties of the limit network model are established.
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