Gulyaev, V. I.; Zubritskaya, A. L.; Koshkin, V. L. Construction of multiple-period-increase bifurcations for solutions of nonlinear ordinary differential equations. (English. Russian original) Zbl 0697.34019 Differ. Equations 25, No. 6, 662-665 (1989); translation from Differ. Uravn. 25, No. 6, 929-933 (1989). The solution of differential equations of the form \(x'=f(x,\lambda,t)\), subject to the periodicity condition \(x(0)=x(x(0),\lambda,T)\), where \(\lambda\) is a bifurcation parameter, is considered. A sequence of approximate solutions is determined by a linearization technique and then extrapolated by difference correction. The technique is then applied to the solution of \(x''+x-x^ 3=\lambda \sin (\omega t)\), \(\omega =1,3\), to demonstrate periodic bifurcations and rapid convergence of the technique. The resulting orbits are also shown and discussed. Reviewer: D.A.Quinney Cited in 1 Document MSC: 34A34 Nonlinear ordinary differential equations and systems 34C25 Periodic solutions to ordinary differential equations 34B99 Boundary value problems for ordinary differential equations 65L10 Numerical solution of boundary value problems involving ordinary differential equations Keywords:bifurcation parameter; approximate solutions; linearization technique; periodic bifurcations PDFBibTeX XMLCite \textit{V. I. Gulyaev} et al., Differ. Equations 25, No. 6, 662--665 (1989; Zbl 0697.34019); translation from Differ. Uravn. 25, No. 6, 929--933 (1989)