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**Stability and bifurcation analysis of a three-dimensional recurrent neural network with time delay.**
*(English)*
Zbl 1235.93191

Summary: We consider the nonlinear dynamical behavior of a three-dimensional recurrent neural network with time delay. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Applying the nor- mal form method and center manifold theory, we obtain some local bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution. Some numerical examples are also presented to verify the theoretical analysis.

### MSC:

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

37N35 | Dynamical systems in control |

37G99 | Local and nonlocal bifurcation theory for dynamical systems |

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\textit{Y. Li}, J. Appl. Math. 2012, Article ID 357382, 13 p. (2012; Zbl 1235.93191)

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### References:

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