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.
Complex-valued Neural network Diffusion Stability Hopf bifurcation Time delay
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This work was supported in part by the National Natural Science Foundation of China under Grant 61503310 and 61402381, in part by the supported by the Fundamental Research Funds for the Central Universities under Grant XDJK2017D170 and XDJK2017D183, in part by China Postdoctoral Foundation under Grant 2016M600720, in part by Chongqing Postdoctoral Project under Grant Xm2016003.
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