盒中腦神經(jīng)網(wǎng)絡(luò)的穩(wěn)定性分析
STABILITY ANALYSIS OF BRAIN-STATE-IN-A-BOX NEURAL NETWORKS
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摘要: 該文對盒中腦(BSB)神經(jīng)網(wǎng)絡(luò)在超立方體內(nèi)的平衡點的漸近穩(wěn)定性進(jìn)行了新的分析，利用Ostrowski定理及相似變換得到了判定平衡點為漸近穩(wěn)定的幾個充分條件。為了說明所提出新方法的有效性，給出了模擬例子。
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關(guān)鍵詞:
- 神經(jīng)網(wǎng)絡(luò);盒中腦;漸近穩(wěn)定性
Abstract: This paper presents a novel asymptotical stability analysis of the equilibrium points in the unit hypercube for the Brain-State-in-a-Box neural model. Some sufficient conditions for the asymptotical stability of equilibrium points are derived using Ostrowskis theorem and the similarity transformation approach. Simulation examples are given to illustrate the effectiveness of new analysis method. -
Anderson J A, Silverstein J W, Ritz S A, et al. Distinctive features, categorical perception and probability learning: Some applications of a neural model, in Neurocomputing: Foundations of Research,Anderson J A and Rosenfeld E. Eds. Cambridge, MA: MIT Press, 1988, Ch.2-Ch.4.[2]Golden R M .The Brain-State-in-a-Box neural model is a gradient descent algorithm[J].Journal of Mathematical Psychology.1986, 30(1):73-80[3]Greenberg H J. Equilibria of the Brain-State-in-a-Box (BSB) neural mode. IEEE Trans.on Neural Networks, 1988, 1(4): 323-324.[4]Trans. on Neural Networks, 1992, 3(1): 86-94.[5]Lillo W E, Miller D C, Hui S, Zak S H. Synthesis of Brain-State-in-a-Box (BSB) based associative memories, IEEE Trans[J].on Neural Networks.1994, 5(5):730-734[6]黃琳．系統(tǒng)與控制理論中的線性代數(shù)．北京：科學(xué)出版社，1986，第5章．[7]張錦炎．常微分方程幾何理論與分支問題．北京：北京大學(xué)出版社，1981，第9章. -
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