Brain as one of the most important organs of the human has gained widely attentions and explorations. Neuron is the functional unit in the brain, and human being typically has around 100 billion neurons in the brain. With the couplings and interactions among such huge quantity of neurons in distinct cortical regions, our brain accomplishes from data collecting, data transferring, data analysing, and finally comes the brain responses. In this thesis,  we want to figure out how different neuron populations interact with each other, and simulate this kind of dynamics of the neurons with Continuous Attractor Neural Networks (CANNs). First we generalize the single layer CANNs to bimodular structure, simulating two sensory modalities in the neural network. Second, we explore the dynamics of the bimodular CANNs when applied with different kinds of stimuli and under various neuron couplings. We begin with applying two static stimuli on two neural layers respectively in the network model, and by adjusting the inter-modular couplings to vary the influence between two neural modalities. We find there are competitions between the external input and the inter-modular couplings within each neural modality. After mastering the dynamics of the bimodular CANNs under static stimuli, we further continue to study the dynamics of the network when applied with one static stimulus and one moving stimulus. The module applied with moving stimulus shows abundant dynamics in its tracking behaviors when accompanied with various inter-modular couplings.  Finally, we fit the bimodular CANNs model to sensory illusion experiment, simulating interactions between two different sensory modalities, illustrating the probable mechanism behind the biological phenomenon. 

Bimodular CANNs show that the couplings between neural populations play crucial roles in transferring information and even in determining responses of neurons, which attracts our attentions to study further.  Besides the couplings among neurons, we are also interested in the couplings between cells in retina. Our collaborator, Prof. C. K. Chan's group from Institute of Physics, Academia Sinica did experiments on bullfrog. They find that when the bullfrog retina is shown a moving bar whose positions are in form of Hidden Markov Model (HMM), the responses of retina, specifically, the last layer cells in retina, ganglion cells, contain information about the future inputs, meaning the retina is not merely an station receiving signals and transferring information to the visual cortex, but also able to analyze information and make predictions about the future inputs based on what it has received. However, this predictive effect can be achieved in HMM because the HMM system carries inertia information. The moving velocity as a hidden variable in HMM is also transferred in each time step, giving the momentum info to the next moment. If the moving bar positions shown to retina do not contain momentum or inertia information, e.g. Ornstein–Uhlenbeck process (OU process), the retina will lose the ability to make  predictions. This property has been discovered in both experiments and our simulations. Experiments have proved that the `predictive' task is accomplished mainly by two neural populations in retina: ganglion cells and amacrine cells, which are the last two layers of cells in retina. Therefore, in our simulations of the predictive effect in retina, we consider two neural populations in the neural network, corresponding to ganglion cells and amacrine cells respectively. We construct the neural network model and the couplings among the neurons according to the measurements from experiments, and our  simulation results show that our neural network model fits with experiments very well.