Displaying similar documents to “Limit cycles in a Kolmogorov-type model.”

Limit cycles in the Holling-Tanner model.

Armengol Gasull, Robert E. Koolj, Joan Torregrosa (1997)

Publicacions Matemàtiques

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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.

Local Collapses in the Truscott-Brindley Model

I. Siekmann, H. Malchow (2008)

Mathematical Modelling of Natural Phenomena

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Relaxation oscillations are limit cycles with two clearly different time scales. In this article the spatio-temporal dynamics of a standard prey-predator system in the parameter region of relaxation oscillation is investigated. Both prey and predator population are distributed irregularly at a relatively high average level between a maximal and a minimal value. However, the slowly developing complex pattern exhibits a feature of “inverse excitability”: Both populations show collapses...

Homoclinic orbits in a two-patch predator-prey model with Preisach hysteresis operator

Alexander Pimenov, Dmitrii Rachinskii (2014)

Mathematica Bohemica

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Systems of operator-differential equations with hysteresis operators can have unstable equilibrium points with an open basin of attraction. Such equilibria can have homoclinic orbits attached to them, and these orbits are robust. In this paper a population dynamics model with hysteretic response of the prey to variations of the predator is introduced. In this model the prey moves between two patches, and the derivative of the Preisach operator is used to describe the hysteretic flow...