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Bifurcation analysis and spatio-temporal patterns of nonlinear oscillations in a delayed neural network with unidirectional coupling. (English) Zbl 1171.34058
A delayed neural network with unidirectional coupling is studied. Stability and Hopf bifurcations for such network are investigated by means of the normal form theory and central manifold theorem. Spatio-temporal patterns of bifurcating periodic oscillations are obtained by use of both symmetric bifurcation theory and the representation theory of Lie groups. Numerical simulations confirm the obtained theoretical results.
MSC:
34K60Qualitative investigation and simulation of models
92B20General theory of neural networks (mathematical biology)
34K20Stability theory of functional-differential equations
37G40Symmetries, equivariant bifurcation theory
34K18Bifurcation theory of functional differential equations
34K19Invariant manifolds (functional-differential equations)
34K13Periodic solutions of functional differential equations
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