Stability Conditions for Two Predator One Prey Systems

M. Farkas and H. I. Freedman
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M. Farkas: Budapest University of Technology, Department of Mathematics
H. I. Freedman: University of Alberta, Department of Mathematics

A chapter in Evolution and Control in Biological Systems, 1989, pp 3-10 from Springer

Abstract: Abstract Consider the predator-prey system (1.1) $$ \mathop{x}\limits^{\bullet } = xF(x,y),\quad \mathop{y}\limits^{\bullet } = yG(x,y) $$ where F, G∈C1, (1.2) $$ F(0,0) > 0,\;\exists K > 0:F(K,0) = 0,\;{F_x}(x,0) \leqslant 0,\;{F_y}(x,y) 0,\;{G_y}(x,y) \leqslant 0 $$ . Assume that there exists an equilibrium E = (x 0 ,y 0 ) in the interior of the positive quadrant of the x,y plane, i.e. x 0 ,y 0 > 0, F(x 0 ,y 0 ) = G(x 0 ,y 0 ) = 0.

Keywords: 92A17; predator-prey systems; asymptotical stability; global stability (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-94-009-2358-4_2

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