Dong, Lingzhen; Chen, Lansun A periodic predator-prey-chain system with impulsive perturbation. (English) Zbl 1159.34327 J. Comput. Appl. Math. 223, No. 2, 578-584 (2009). Summary: A periodic predator-prey-chain system with impulsive effects is considered. By using the global results of Rabinowitz and standard techniques of bifurcation theory, the existence of its trivial, semi-trivial and nontrivial positive periodic solutions is obtained. It is shown that the nontrivial positive periodic solution for such a system may be bifurcated from an unstable semi-trivial periodic solution. Furthermore, the stability of these periodic solutions is studied. Cited in 6 Documents MSC: 34C60 Qualitative investigation and simulation of ordinary differential equation models 34A37 Ordinary differential equations with impulses 92D25 Population dynamics (general) 34C23 Bifurcation theory for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations Keywords:predator-prey chain; bifurcation; impulsive perturbation; positive periodic solution; noncritical solution PDFBibTeX XMLCite \textit{L. Dong} and \textit{L. Chen}, J. Comput. Appl. Math. 223, No. 2, 578--584 (2009; Zbl 1159.34327) Full Text: DOI References: [1] Bardi, Martino, Predator-prey models in periodically fluctuating environment, J. Math. Biol., 12, 127-140 (1981) · Zbl 0466.92019 [2] Cushing, Two species competition in a periodic environment, J. Math. Biol., 10, 384-400 (1980) · Zbl 0455.92012 [3] Zhang, Zhengqiu; Wang, Zhicheng, Periodic solution for a two-species nonautonomous competition Lotka-Volterra Patch system with time delay, J. Math. Anal. Appl., 265, 38-48 (2002) · Zbl 1003.34060 [4] Hui, Jing; Chen, Lansun, Existence of positive periodic solution of periodic time-dependent predator-prey system with impulsive effects, Acta Math. Sin. (Engl. Ser.), 20, 423-432 (2004) · Zbl 1058.34051 [5] Lakmeche, A.; Arino, O., Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment, Dyn. Contin. Discrete Impuls. Syst., 7, 265-298 (2000) · Zbl 1011.34031 [6] Tang, Sanyi; Chen, Lansun, The periodic predator-prey Lotka-Volterra model with impulsive effect, J. Mech. Med. Biol., 2, 3-4, 267-296 (2002) [7] Bainov, D. D.; Simeonov, P. S., Impulsive Differential Equations: Periodic Solutions and Applications (1993), Longman: Longman England · Zbl 0793.34011 [8] Rabinowitz, P. H., Some global results of nonlinear eigenvalue problems, J. Funct. Anal., 7, 487-513 (1971) · Zbl 0212.16504 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.