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Linear stability and Hopf bifurcation in a delayed two-coupled oscillator with excitatory-to-inhibitory connection. (English) Zbl 1205.34107
This paper deals with the dynamical behaviour of a delayed two-coupled oscillator with excitatory-to-inhibitory connection. Some parameter regions are given for linear stability, absolute synchronization and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. The authors also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using symmetric bifurcation theory of delay differential equations with representation theory of Lie groups. The paper ends with some numerical simulations to illustrate the theoretical results.

34K60Qualitative investigation and simulation of models
34K20Stability theory of functional-differential equations
34K18Bifurcation theory of functional differential equations
34K17Transformation and reduction of functional-differential equations and systems; normal forms
34K19Invariant manifolds (functional-differential equations)
34C15Nonlinear oscillations, coupled oscillators (ODE)
Full Text: DOI
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