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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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##### References:
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