Stability and periodic oscillations in the Moon-Rand systems

DOI10.1016/j.nonrwa.2012.06.005zbMath1264.34059OpenAlexW2033441253MaRDI QIDQ1926428

Douglas S. Shafer, Adam Mahdi, Valery G. Romanovski

Publication date: 28 December 2012

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2012.06.005

zbMATH Keywords

stabilityintegrabilitycenter problemcyclicityMoon-Rand system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Invariant manifolds for ordinary differential equations (34C45)

Related Items (14)

Rigid centres on the center manifold of tridimensional differential systems ⋮ The generalized polynomial Moon-Rand system ⋮ The connection between the dynamical properties of 3D systems and the image of the energy-Casimir mapping ⋮ Center problem in the center manifold for quadratic and cubic differential systems in \(\mathbb{R}^3\) ⋮ Center problem in the center manifold for quadratic differential systems in \(\mathbb{R}^3\) ⋮ The Hopf bifurcation in the Shimizu-Morioka system ⋮ Linearization of non-degenerate analytic centres in ⋮ A hybrid symbolic-numerical approach to the center-focus problem ⋮ Cyclicity of polynomial nondegenerate centers on center manifolds ⋮ Hopf bifurcation of a generalized Moon-Rand system ⋮ Differential Galois integrability obstructions for nonlinear three-dimensional differential systems ⋮ Ten limit cycles around a center-type singular point in a 3-d quadratic system with quadratic perturbation ⋮ Identifying weak foci and centers in the Maxwell-Bloch system ⋮ Limit cycles bifurcations for a class of 3-dimensional quadratic systems

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