Dynamics of a two-neuron system with discrete and distributed delays.

*(English)*Zbl 1049.92004Summary: We consider a two-neuron network model with multiple discrete and distributed delays, where the distributed delays describe the neural feedback and the discrete delays describe the neural interaction history. Three special cases of the artificial neural network model are considered. The first case corresponds to two neural interactions with instantaneous feedback for each neuron and neural interaction history. The second case corresponds to two neural interactions with delayed neural feedback and no neural interaction history. The last case corresponds to two neural interactions with delayed neural feedback and neural interaction history. Local stability analyses are carried out for all three cases. Numerical simulations are performed to illustrate the obtained results.

##### MSC:

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

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

34K20 | Stability theory of functional-differential equations |

##### Keywords:

Two-neuron system; Discrete and distributed delays; Neural feedback; Neural interaction history
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\textit{S. Ruan} and \textit{R. S. Filfil}, Physica D 191, No. 3--4, 323--342 (2004; Zbl 1049.92004)

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