Periodic orbits in 3-dimensional systems and application to a perturbed Volterra system

DOI10.1016/j.jde.2015.10.018zbMath1382.34033OpenAlexW2175342941MaRDI QIDQ897815

Yicang Zhou, Chengzhi Li, Zhien Ma

Publication date: 7 December 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2015.10.018

zbMATH Keywords

bifurcationperiodic orbitinvariant manifoldVolterra system

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (8)

Complex dynamics in a generalized Langford system ⋮ Bifurcation of periodic orbits by perturbing high-dimensional piecewise smooth integrable systems ⋮ Bifurcation from Periodic Orbits of n-Dimensional Piecewise Smooth Differential Systems with Two Switching Planes ⋮ On the Number of Limit Cycles Bifurcated from a Near-Hamiltonian System with a Double Homoclinic Loop of Cuspidal Type Surrounded by a Heteroclinic Loop ⋮ PERIODIC ORBIT OF THE PENDULUM WITH A SMALL NONLINEAR DAMPING ⋮ Bifurcation of periodic orbits of a three-dimensional piecewise smooth system ⋮ Bifurcation and number of subharmonic solutions of a \(2n\)-dimensional non-autonomous system and its application ⋮ On the number of zeros of Abelian integral for a class of cubic Hamiltonian systems

Cites Work

• Unnamed Item
• Limit cycles of differential equations
• Hopf-Takens bifurcations and centres
• A criterion for determining the monotonicity of the ratio of two Abelian integrals
• Abelian integrals and limit cycles

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