Bifurcation Analysis of Delayed Complex-Valued Neural Network with Diffusions

摘要

In this paper, a class of delayed complex-valued neural network with diffusion under Dirichlet boundary conditions is considered. By using the properties of the Laplacian operator and separating the neural network into real and imaginary parts, the corresponding characteristic equation of neural network is obtained. Then, the dynamical behaviors including the local stability, the existence of Hopf bifurcation of zero equilibrium are investigated. Furthermore, by using the normal form theory and center manifold theorem of the partial differential equation, the explicit formulae which determine the direction of bifurcations and stability of bifurcating periodic solutions are obtained. Finally, a numerical simulation is carried out to illustrate the results.