Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay

[摘要] We consider the nonlinear dynamical behavior of athree-dimensional recurrent neural network with time delay. By choosing thetime delay as a bifurcation parameter, we prove that Hopf bifurcation occurswhen the delay passes through a sequence of critical values. Applying the nor-mal form method and center manifold theory, we obtain some local bifurcationresults and derive formulas for determining the bifurcation direction and thestability of the bifurcated periodic solution. Some numerical examples are alsopresented to verify the theoretical analysis.

[学科分类] 应用数学