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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.

34K60 Qualitative investigation and simulation of models involving functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34K20 Stability theory of functional-differential equations
37G40 Dynamical aspects of symmetries, equivariant bifurcation theory
34K18 Bifurcation theory of functional-differential equations
34K19 Invariant manifolds of functional-differential equations
34K13 Periodic solutions to functional-differential equations
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