Collective Dynamics and Computational Properties of Small Neural Networks

神经网络研究的一个主要挑战是建立足够简单的模型来进行分析，但要描述网络的生物行为，并可以进行实验测试。最近对小型神经网络的实验和理论研究使这种模型的建立成为可能。在本研究中，我们将建立龙虾幽门中枢模式产生器的详细生物学模型。这个模型将是霍奇金-赫胥黎模型的扩展版本，包括重要的电流和突触连接。利用动力系统理论和物理近似的方法，我们将得到一个更简单的模型，它仍然能描述实验结果。阶段模型将由完整模型发展而来。将测试突触修饰的影响和神经元固有特性的变化，并研究神经递质的影响。理论研究将结合神经网络和动力系统理论的分析和数值方法，数值模拟，并将与神经生物学实验进行比较。这项研究将有助于弥合常规神经网络模型与生物现实之间的差距。

A major challenge in neural network research is to build models that are simple enough for analysis but describe the biological behavior of the network and can be tested experimentally. Recent experimental and theoretical studies of small neural networks make the building of such models possible. In the proposed research we will build a detailed biological model of the pyloric Central Pattern Generator of the lobster. This model will be an extended version of the Hodgkin-Huxley model which includes the important currents and synaptic connections. Using methods from dynamical system theory and physical approximation we will obtain a simpler model which still describes the experimental results. A phase model will be developed from the full model. The effects of synaptic modification and changes of intrinsic properties of the neurons will be tested, and the effect of neurotransmitters will be investigated. The theoretical study will combine analytical and numerical methods from neural network and dynamical system theory, numerical simulations and will be compared to neurobiological experiments. The research will contribute to bridging the gap between regular neural network models and the biological reality.