ニューラルネットワークにおける解の分岐現象について

概要

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In order to understand the global behavior of nonlinear dynamical networks, it is very important to understand the equilibrium points and their basin attractions. In this paper, we propose a method to find the bifurcation points on the solution curves. Now, consider the following nonlinear equation:f(x,α)=0,f:R^n×R^1→R^n (1) We apply an arc-length method to trace the solution curve. Then the first (n×n) Jacobian matrix at limit point becomes singular but (n+1)×(n+1) matrix is nonsingular, so that we can trace the curve continuously. On the other hand, at bifurcation point,(n+1)×(n+1) Jacobian matrix becomes singular and the determinant changes the sign so that we can easily find the bifurcation points on the solution curve. We apply the technique to analysis of six-neurons Hopfield network.
社団法人電子情報通信学会の論文
1995-03-27