Period annulus of a Lotka–Volterra system

doi:10.1088/0951-7715/22/12/009

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

Chengzhi Li et al 2009 Nonlinearity 22 2971-2979 doi: 10.1088/0951-7715/22/12/009

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Chengzhi Li¹ and Jaume Llibre²
¹ LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China
² Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Catalonia, Spain
E-mail: licz@math.pku.edu.cn and jllibre@mat.uab.es

Recommended by C-Q Cheng

Abstract. 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.

Mathematics Subject Classification: 34C07, 34C08, 37G15

Print publication: Issue 12 (December 2009)
Received 14 December 2008, in final form 7 October 2009
Published 30 October 2009

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

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