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Zbl 0941.65132
Ford, Neville J.; Wulf, Volker
The use of boundary locus plots in the identification of bifurcation points in numerical approximation of delay differential equations. (English)
[J] J. Comput. Appl. Math. 111, No.1-2, 153-162 (1999). ISSN 0377-0427

The subject are nonlinear delay differential equations which have a Hopf bifurcation point lying on the boundary of the region of asymptotic stability for the zero solution which is a steady state for the problem. The boundary locus method is used as a tool for identifying the stability domain of delay differential equations and their numerical analogue, and for identifying particular parameter values at which Hopf bifurcation arises. It is demonstrated that, for consistent and stable linear multistep methods, Hopf bifurcation points in the numerical schemes approximate the true Hopf bifurcation point with accuracy of the order of the numerical methods.
[D.Petcu (Timişoara)]

MSC 2000:: *65P30 Bifurcation problems
37M20 Computational methods for bifurcation problems
34K18 Bifurcation theory of functional differential equations
65L06 Multistep, Runge-Kutta, and extrapolation methods
65L20 Stability of numerical methods for ODE
65P40 Nonlinear stabilities
37G10 Bifurcations of singular points

Keywords: nonlinear delay differential equations; boundary locus method; Hopf bifurcation points; asymptotic stability; linear multistep methods

Cited in: Zbl 1161.65056

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