Krasnosel’skij, M. A.; Kuznetsov, N. A.; Yumagulov, M. G. Localization and construction of cycles in Hopf’s bifurcation at infinity. (English. Russian original) Zbl 0880.34038 Dokl. Math. 52, No. 2, 223-226 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 344, No. 4, 446-449 (1995). Consider the \(n\)-dimensional autonomous differential system \[ dx/dt= A(\lambda)x+ f(x,\lambda)\tag{\(*\)} \] under the following assumptions:(i) \(\lambda\) is a scalar parameter,(ii) \(A:\mathbb{R}\to L(\mathbb{R}^n,\mathbb{R}^n)\) is continuous, \(A(\lambda_0)\) has a pair of simple pure imaginary eigenvalues \(\pm i\omega_0\), \(\omega_0>0\); \(0\) and \(\pm k\omega_0 i\) \((k=2,3,\dots)\) are no eigenvalues of \(A(\lambda_0)\).(iii) \(\lim_{|x|\to\infty}\max_{|\lambda-\lambda_0|\leq 1}{|f(x,\lambda)|\over|x|}= 0\).The authors study Hopf bifurcation from infinity by means of an equivalent integral equation. To approximate the bifurcating cycle, the method of functionalization of parameters and the Newton-Kantorovič method is used. Reviewer: K.R.Schneider (Berlin) Cited in 2 Documents MSC: 34C23 Bifurcation theory for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations Keywords:Hopf bifurcation from infinity; functionalization of parameters; Newton-Kantorovič method PDFBibTeX XMLCite \textit{M. A. Krasnosel'skij} et al., Dokl. Math. 52, No. 2, 223--226 (1995; Zbl 0880.34038); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 344, No. 4, 446--449 (1995)