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Stability and Neimark-Sacker bifurcation of numerical discretization of delay differential equations. (English) Zbl 1198.65107
Summary: A kind of a discrete delay model obtained by Euler method is investigated. Firstly, the linear stability of the model is studied. It is found that there exist Neimark-Sacker bifurcations when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction and stability of the Neimark-Sacker bifurcations are derived by using the normal form theory and center manifold theorem. Finally, computer simulations are provided to illustrate the analytical results found.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
65L03 Numerical methods for functional-differential equations
65P30 Numerical bifurcation problems
37G99 Local and nonlocal bifurcation theory for dynamical systems
34K18 Bifurcation theory of functional-differential equations
34K20 Stability theory of functional-differential equations
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