Simulations Of Dynamical Phenomena And Decision-making Tasks In Neural Network Models

Various functions of the brain, such as learning, memory and cognition, emotion, are completed by neural networks which are composed of a large number of interacting neurons. Thus, it is crucial to research the theoretical neural network for understanding the function of the brain. This thesis mainly presents the simulations and dynamical analysis of three neural circuits:a local microcircuit in pre-Botzinger complex, a tail-withdraw reflex circuit in Aplysia and a learning-based network in Frontal eye fields. The main work of this dissertation are as follows.In Chapter 1, we mainly introduce the background, research developments of the neural network model and the introduction of the main content of this paper.In Chapter 2, we introduce the preliminary knowledge and research basis about the neural network model researching. These contents include the basic structure and the mathematical models of neurons; ion channels and their mathematical models; the excitability of neurons; synapses and their mathematical models; the synaptic plasticity; the topological structure of neural circuits; a number of classical neural circuits; the latest research progresses in computational neuroscience. The mathematical models of neurons include four conductance-based models:Hodgkin-Huxley model, Connor-Stevens model, Morris-Lecar model and respiratory neuron model; integrate-and-fire model; the Rail cable model and its discrete form-multi-compartment model. The synapses include electrical synapse and chemical synapse.In Chapter 3, we study the local neural circuit, mainly discuss the phase synchro-nization of the coupled respiratory neurons. First, a coupled respiratory neurons model is constructed by using a electrical synapse to couple two respiratory neurons. After contrasting electrical discharges between the single neuron model and the coupled neu-rons model, we find that the coupled neurons model exhibits a more complex transition pattern of the firing patterns. When varying the coupling strength and membrane capac-itance, the coupled system exhibits different synchronization states and the transitions between them. Further more, we present the distribution of the synchronization state in a two-dimensional plane of coupling strength and membrane capacitance, and conclude the rhythm of the transitions of synchronization states.In Chapter 4, we study the tail-withdrawal reflex circuit in Aplysia. After researching the characteristics of sensory neurons waveform, the rhythms of the reflex circuit are obtained by applying different stimulation strengthes and stimulating different number of sensory neurons. In addition, we connect neural circuit of the reflex to a muscle fiber model, and successfully simulate the excitation-contraction coupling between neural signals and muscle fiber. Finally, the effect of the synaptic plasticity on the long-lasting response in motor neuron is also discussed. These results reveal the characteristics of the tail-withdrawal reflex circuit in Aplysia.In Chapter 5, we extend a layered model of the frontal eye field model with three aspects:direction-preferred populations that cluster together the neurons with the same orientation preference, rule modules that control different rule-dependent activities, and reward-based synaptic plasticity that modulates connections to flexibly change the de-cision according to task demands, and finally construct a learning-based neural network model of the frontal eye fields. Based on this extended neural circuit, we simulate three decision choice tasks:an anti-saccade task, a no-go task, and an associative task. We find that the synaptic plasticity can modulate the competition of choices by suppressing erroneous choices while enhancing the correct (rewarding) choice. In addition, the trained model capture some properties exhibited in animal and human experiments, such as the latency of the reaction time distribution of anti-saccades, the stop signal mechanism for canceling a reflexive saccade, and the variation of latency to half-max selectivity. Fur-thermore, the trained model is capable of reproducing the re-learning procedures when switching tasks and reversing the cue-saccade association. These results disclose the decision process and rhythms of cognition of brain in decision-making tasks.