A Quadratic System with a Nonmonotonic Period Function

DOI10.2307/2047250zbMath0651.34043OpenAlexW4249365489MaRDI QIDQ3796013

Freddy Dumortier, Carmen C. Chicone

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2047250

zbMATH Keywords

centerperiodic trajectories

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) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (16)

First derivative of the period function with applications ⋮ Finiteness for critical periods of planar analytic vector fields ⋮ The period function of potential systems of polynomials with real zeros ⋮ Monotonicity of the period function of the Liénard equation of second kind ⋮ The period function of Hamiltonian systems with separable variables ⋮ regularity properties of the period function near a center of a planar vector field ⋮ The period functions' higher order derivatives ⋮ Separable solutions of some quasilinear equations with source reaction ⋮ The period function of the generalized Lotka-Volterra centers ⋮ Properties of the period function for some Hamiltonian systems and homogeneous solutions of a semilinear elliptic equation ⋮ The period function for quadratic integrable systems with cubic orbits ⋮ The period function of reversible quadratic centers ⋮ The period function of reversible Lotka-Volterra quadratic centers ⋮ LOCAL BIFURCATION OF CRITICAL PERIODS IN QUADRATIC-LIKE CUBIC SYSTEMS ⋮ Bifurcation of Critical Periods for Plane Vector Fields ⋮ The monotonicity of period function for the codimension four quadratic system \(Q_4\).

Cites Work

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• The period in the Lotka-Volterra system is monotonic
• Thermodynamics, real and complex periods of the Volterra model
• On the number of critical points of the period
• The monotonicity of the period function for planar Hamiltonian vector fields
• The Period in the Volterra–Lotka Predator-Prey Model
• Global behaviour of solution branches for some Neumann problems depending on one or several parameters.
• A class of Hamiltonian systems with increasing periods.

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