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The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system

Chengzhi Li1 and Jaume Llibre2

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Recommended by C-Q Cheng

We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka–Volterra differential system \dot x=y+\case{3}{2}(x^2-y^2) , \dot y=-x(1-y) , inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles.


PACS

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

02.30.Hq Ordinary differential equations

02.30.Oz Bifurcation theory

MSC

37G15 Bifurcations of limit cycles and periodic orbits

34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 12 (December 2009)

Received 14 December 2008, in final form 7 October 2009

Published 30 October 2009



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