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**Hopf bifurcation and stability for a delayed tri-neuron network model.**
*(English)*
Zbl 1175.37086

Summary: A neural network model with three neurons and a single time delay is considered. Its linear stability is investigated and Hopf bifurcations are demonstrated by analyzing the corresponding characteristic equation. In particular, the explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and the center manifold theorem. In order to illustrate our theoretical analysis, some numerical simulations are also included in the end.

### MSC:

37N25 | Dynamical systems in biology |

34K13 | Periodic solutions to functional-differential equations |

34K18 | Bifurcation theory of functional-differential equations |

92C20 | Neural biology |

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\textit{X.-P. Yan}, J. Comput. Appl. Math. 196, No. 2, 579--595 (2006; Zbl 1175.37086)

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