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Qualitative properties of two-dimensional predator-prey systems. (English) Zbl 0883.34040
This paper investigates the number and uniqueness of limit cycles appearing in two-dimensional predator-prey system: \[ \dot x=x \varphi(x)- p(x)y, \quad \dot y=y [-\psi (y)+ p(x)] \] for some specific choice of functions:
(i) \(\psi(y) =C_0\), \(p(x)= x^n/(b+x^n)\), \(\varphi(x)\) arbitrary;
(ii) \(\psi(y) =C_0+ C_1 y\), \(p(x) =x/(b+x)\), \(\varphi (x)=k\);
(iii) \(\psi(y)\) arbitrary, \(p(x)= x/(b+x)\), \(\varphi (x)=k\).
This paper also gives several examples of systems with at least two limit cycles.

MSC:
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
92D25 Population dynamics (general)
92B05 General biology and biomathematics
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