| Summary: | 碩士 === 國立高雄大學 === 應用數學系碩士班 === 102 === In this thesis, we utilize Monte Carlo simulation method to study the effect of white noise on the qualitative behavior of adaptive winner-take-all neural network model, and try to use the simulation results to characterize the effect of white noise on the dynamical mechanisms underlying the random switching of visual perception in the binocular rivalry phenomenon. By observing and characterizing the qualitative change in the empirical probability density functions of simulated data, we find that the white noise intensity can make the system to generate so-called phenomenological bifurcation, which makes a transition for the system from fluctuation around the stable state random switching between two states. Also, we find that the increase of white noise intensity can lead to a change for the range at which the phenomenological bifurcation occurs for one important dynamical parameter--adaptation strength. Furthermore, under the assumption of Gaussian approximation, we derive the first and second order moment equations for the stochastic differential equations, which can provide an analytic tool for advanced bifurcation analysis of the system in the future.
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