Dynamics of a system exhibiting the global bifurcation of a limit cycle at infinity

DOI10.1016/0020-7462(85)90040-XzbMath0647.34033OpenAlexW2043180536MaRDI QIDQ1104469

W. L. Keith, Richard H. Rand

Publication date: 1985

Published in: International Journal of Non-Linear Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-7462(85)90040-x

zbMATH Keywords

limit cyclesglobal bifurcationscenter manifold theoryRayleigh equationVan der Pol equationsLindstedt perturbation methodPoincaré- Bendixson theorem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Local and nonlocal bifurcation theory for dynamical systems (37G99) Numerical analysis in abstract spaces (65J99)

Related Items (6)

Bifurcation of limit cycles at infinity in a class of switching systems ⋮ Hopf bifurcation at infinity in 3D symmetric piecewise linear systems. Application to a Bonhoeffer-van der Pol oscillator ⋮ Determinacy of degenerate equilibria with linear part \(x'=y\), \(y'=0\) using MACSYMA ⋮ EXISTENCE AND STABILITY OF PERIODIC SOLUTIONS OF A RAYLEIGH TYPE EQUATION ⋮ Existence of asymptotically stable periodic solutions of a Rayleigh type equation ⋮ Bifurcation of a periodic orbit from infinity in planar piecewise linear vector fields

Uses Software

• MACSYMA

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