Geodesic
Positive periodic solution for ratio-dependent $n$-species discrete time system
Applications of Mathematics, Tome 56 (2011) no. 6, pp. 577-589.

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In this paper, sharp a priori estimate of the periodic solutions is obtained for the discrete analogue of the continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modelling the dynamics of the $n-1$ competing preys and one predator having nonoverlapping generations. Based on more precise a priori estimate and the continuation theorem of the coincidence degree, an easily verifiable sufficient criterion of the existence of positive periodic solutions is established. The result obtained in this paper greatly improves the existing results.
DOI : 10.1007/s10492-011-0034-z
Classification : 34C25, 39A12, 39A22, 39A23, 92D25
Keywords: ratio-dependent; predator-prey system; periodic solution; a priori estimate 
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     title = {Positive periodic solution for ratio-dependent $n$-species discrete time system},
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Tang, Mei-Lan; Liu, Xin-Ge. Positive periodic solution for ratio-dependent $n$-species discrete time system. Applications of Mathematics, Tome 56 (2011) no. 6, pp. 577-589. doi : 10.1007/s10492-011-0034-z. http://geodesic.mathdoc.fr/articles/10.1007/s10492-011-0034-z/

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