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白噪聲對雙眼競爭神經網路模型動態機制的影響 = The Effect o...

國立高雄大學應用數學系碩士班

白噪聲對雙眼競爭神經網路模型動態機制的影響 = The Effect of White Noise on the Dynamical Mechanism in the Neural Network Model for Binocular Rivalry

紀錄類型:	書目-語言資料,印刷品 : 單行本
並列題名:	The Effect of White Noise on the Dynamical Mechanism in the Neural Network Model for Binocular Rivalry
作者:	邱俊豪,
其他團體作者:	國立高雄大學
出版地:	[高雄市]
出版者:	撰者;
出版年:	2014[民103]
面頁冊數:	37面彩圖，表 : 30公分;
標題:	適應性贏者全拿神經網路模型
標題:	Adaptive Winner-Take-All Model
電子資源:	http://handle.ncl.edu.tw/11296/ndltd/48133339747220894428
附註:	參考書目：面31-32
附註:	103年12月16日公開
摘要註:	本論文利用蒙地卡羅數值模擬方法研究適應性贏者全拿(Adaptive Winner-Take-All)神經網路模型在白噪聲影響下定性行為上的變化，並以模擬結果來試著刻畫白噪聲在雙眼競爭視覺隨機交替之潛在動態機制的作用。透過觀察和刻畫模擬數據之機率密度函數在定性上的變化，我們發現增加白噪聲強度能引起系統產生所謂的現象分歧(phenomenological bifurcation)，使得系統從隨機穩定的行為轉變成在兩狀態之間隨機交替的行為。同時，我們也發現一個影響此機制的重要動態參數--適應性強度--的分歧區域也會隨著白噪聲強度增加而改變。進一步地，我們在高斯分佈的近似假設下，對此隨機微分方程的一階和二階動差方程式(moment equations)進行推導，以提供未來對此系統做進一步分歧分析的一個解析工具。 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.

白噪聲對雙眼競爭神經網路模型動態機制的影響 = The Effect of White Noise on the Dynamical Mechanism in the Neural Network Model for Binocular Rivalry
邱, 俊豪

白噪聲對雙眼競爭神經網路模型動態機制的影響 = The Effect of White Noise on the Dynamical Mechanism in the Neural Network Model for Binocular Rivalry / 邱俊豪撰 - [高雄市] : 撰者, 2014[民103]. - 37面 ; 彩圖，表 ; 30公分.
參考書目：面31-32103年12月16日公開.
適應性贏者全拿神經網路模型Adaptive Winner-Take-All Model

白噪聲對雙眼競爭神經網路模型動態機制的影響 = The Effect of White Noise on the Dynamical Mechanism in the Neural Network Model for Binocular Rivalry
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330 $a 本論文利用蒙地卡羅數值模擬方法研究適應性贏者全拿(Adaptive Winner-Take-All)神經網路模型在白噪聲影響下定性行為上的變化，並以模擬結果來試著刻畫白噪聲在雙眼競爭視覺隨機交替之潛在動態機制的作用。透過觀察和刻畫模擬數據之機率密度函數在定性上的變化，我們發現增加白噪聲強度能引起系統產生所謂的現象分歧(phenomenological bifurcation)，使得系統從隨機穩定的行為轉變成在兩狀態之間隨機交替的行為。同時，我們也發現一個影響此機制的重要動態參數--適應性強度--的分歧區域也會隨著白噪聲強度增加而改變。進一步地，我們在高斯分佈的近似假設下，對此隨機微分方程的一階和二階動差方程式(moment equations)進行推導，以提供未來對此系統做進一步分歧分析的一個解析工具。 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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