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Stability and bifurcation in a neural network model with two delays. (English) Zbl 1066.34511
Summary: A simple neural network model with two delays is considered. Linear stability of the model is investigated by analyzing the associated characteristic transcendental equation. For the case without self-connection, it is found that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. An example is given and numerical simulations are performed to illustrate the obtained results.

34K18Bifurcation theory of functional differential equations
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
Full Text: DOI
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