Uniqueness of limit cycles in a predator-prey system with Holling-type functional response

Sugie, Jitsuro

doi:10.1090/qam/1770656

Author: Jitsuro Sugie
Journal: Quart. Appl. Math. 58 (2000), 577-590
MSC: Primary 92D25; Secondary 34C05, 34C60
DOI: https://doi.org/10.1090/qam/1770656
MathSciNet review: MR1770656
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Abstract: This paper is concerned with the problem of uniqueness of limit cycles in a predator-prey system with Holling’s functional response ${x^p}/\left ( a + {x^p} \right )$, where $a$ and $p$ are positive parameters. The problem has not yet been settled only in the case $1 < p < 2$. This paper gives a sufficient condition under which the predator-prey system with $1 < \\ p < 2$ has exactly one limit cycle by using a result of Zhang and Gao. Finally, the fact that our condition is also necessary is mentioned.

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