Qualitative Analysis And Appliance Of Locally Coupled Neural Oscillator Network

A lot of neural network models are developed in visual image processing, artificial intelligence and pattern recognition and many other fields. It is of great importance to study dynamical behaviors of these models.In recent years, the locally coupled Wilson-Cowan neural oscillator network model is widely used in associative memory and image processing. It is necessary to understand its internal working mechanism. In this thesis, the locally coupled neural oscillator is studied from the point of view of theoretical analysis. The paper focus on the sufficient conditions under which a single oscillator can oscillate and the sufficient conditions on the coupling parameters which guarantee asymptotically global synchronization of oscillators receiving the same external input. In particular, the influence of the time delay is considered. Taking the time delay as a parameter, the critical value of the time delay that Hopf bifurcation occurs and the areas in parameter space where the Hopf bifurcation occurs are obtained. Then, the matlab programs are used to verify the results. Finally, the neural oscillator network model based on the above analytical results is applied to simple image segmentation. The methods used and the results obtained in this paper are important to future researches.