# Limit cycles in the Holling-Tanner model.

Armengol Gasull; Robert E. Koolj; Joan Torregrosa

Publicacions Matemàtiques (1997)

- Volume: 41, Issue: 1, page 149-167
- ISSN: 0214-1493

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topGasull, Armengol, Koolj, Robert E., and Torregrosa, Joan. "Limit cycles in the Holling-Tanner model.." Publicacions Matemàtiques 41.1 (1997): 149-167. <http://eudml.org/doc/41283>.

@article{Gasull1997,

abstract = {This paper deals with the following question: does the asymptotic stability of the positive equilibrium of the Holling-Tanner model imply it is also globally stable? We will show that the answer to this question is negative. The main tool we use is the computation of Poincaré-Lyapunov constants in case a weak focus occurs. In this way we are able to construct an example with two limit cycles.},

author = {Gasull, Armengol, Koolj, Robert E., Torregrosa, Joan},

journal = {Publicacions Matemàtiques},

keywords = {Formas cuadráticas; Campos vectoriales; Sistemas diferenciales; Ciclos límite; Teorema estabilidad; location of integral curves; singular points; limit cycles},

language = {eng},

number = {1},

pages = {149-167},

title = {Limit cycles in the Holling-Tanner model.},

url = {http://eudml.org/doc/41283},

volume = {41},

year = {1997},

}

TY - JOUR

AU - Gasull, Armengol

AU - Koolj, Robert E.

AU - Torregrosa, Joan

TI - Limit cycles in the Holling-Tanner model.

JO - Publicacions Matemàtiques

PY - 1997

VL - 41

IS - 1

SP - 149

EP - 167

AB - This paper deals with the following question: does the asymptotic stability of the positive equilibrium of the Holling-Tanner model imply it is also globally stable? We will show that the answer to this question is negative. The main tool we use is the computation of Poincaré-Lyapunov constants in case a weak focus occurs. In this way we are able to construct an example with two limit cycles.

LA - eng

KW - Formas cuadráticas; Campos vectoriales; Sistemas diferenciales; Ciclos límite; Teorema estabilidad; location of integral curves; singular points; limit cycles

UR - http://eudml.org/doc/41283

ER -

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