Multiple bifurcation Analysis in a Neural Network Model with Delays

A synchronized neural network model with delays is considered. The bifurcations arising from the zero root of the corresponding characteristic equation have been studied by employing the center manifold theorem, normal form method and bifurcation theory. It is shown that the system may exhibit transcritical/pitchfork bifurcation, or Bogdanov–Takens bifurcation. Some numerical simulation examples are given to justify the theoretical results.

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