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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2019,10]]},"abstract":"<jats:p> Since the electromagnetic field of neural networks is heterogeneous, the diffusion phenomenon of electrons exists inevitably. In this paper, we investigate the existence of Turing\u2013Hopf bifurcation in a reaction\u2013diffusion neural network. By the normal form theory for partial differential equations, we calculate the normal form on the center manifold associated with codimension-two Turing\u2013Hopf bifurcation, which helps us understand and classify the spatiotemporal dynamics close to the Turing\u2013Hopf bifurcation point. 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