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**Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays.**
*(English)*
Zbl 1062.34079

Summary: A delay-differential equation modelling a bidirectional associative memory (BAM) neural network with three neurons is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold reduction. Numerical simulation results are given to support the theoretical predictions.

### MSC:

34K18 | Bifurcation theory of functional-differential equations |

34K19 | Invariant manifolds of functional-differential equations |

34K17 | Transformation and reduction of functional-differential equations and systems, normal forms |

34K13 | Periodic solutions to functional-differential equations |

34K20 | Stability theory of functional-differential equations |

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\textit{Y. Song} et al., Physica D 200, No. 3--4, 185--204 (2005; Zbl 1062.34079)

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