Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1064.92045
Kar, Tapan Kumar
Stability analysis of a prey-predator model incorporating a prey refuge. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 10, No. 6, 681-691 (2005). ISSN 1007-5704

The author analyzes a Lotka-Volterra type predator-prey model with Michaelis-Menten type functional responce. In this model, the population density of the prey is resource limited and each predator's functional responce to the prey approaches a constant as the prey population increases and a spatial refuge protects a constant proportion of prey from predation. A refuge can be important for the biological control of a pest, but increasing the amount of refuge can increase prey densities and lead to population outbreaks. Conditions for existence and stability of the equilibria and persistent criteria for the system are proposed. It is proved that exactly one stable limit cycle occurs in this system when the positive equilibrium is unstable; and local asymptotic stability of the positive equilibrium implies its global asymptotic stability.
[Igor Andrianov (Köln)]

MSC 2000:: *92D40 Ecology
34D05 Asymptotic stability of ODE
92D25 Population dynamics
34C60 Applications of qualitative theory of ODE

Keywords: prey-predator; refuge; stability; persistence; limit cycles

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]