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Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays. (English) Zbl 1062.34079
Summary: A delay-differential equation modelling a bidirectional associative memory (BAM) neural network with three neurons is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold reduction. Numerical simulation results are given to support the theoretical predictions.
MSC:
34K18Bifurcation theory of functional differential equations
34K19Invariant manifolds (functional-differential equations)
34K17Transformation and reduction of functional-differential equations and systems; normal forms
34K13Periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations