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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:
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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