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The use of boundary locus plots in the identification of bifurcation points in numerical approximation of delay differential equations. (English) Zbl 0941.65132
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.

MSC:
65P30Bifurcation problems (numerical analysis)
37M20Computational methods for bifurcation problems
34K18Bifurcation theory of functional differential equations
65L06Multistep, Runge-Kutta, and extrapolation methods
65L20Stability and convergence of numerical methods for ODE
65P40Nonlinear stabilities (numerical analysis)
37G10Bifurcations of singular points