Multiple Positive Periodic Solutions to a Periodic Predator-Prey-Chain Model with Harvesting Terms
In this paper, a class of predator-prey-chain model with harvesting terms are studied. By using Mawhin-s continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient conditions are established for the existence of eight positive periodic solutions. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1329875Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 940
 Martino Bardi, Predator-prey models in periodically fluctuating environment, J. Math. Biol. 12 (1981) 127-140.
 Z. Zhang, Z. Wang, Periodic solution for a two-species nonautonomous competition Lotka-Volterra Patch system with time delay, J. Math. Anal. Appl. 265 (2002) 38-48.
 Cushing, Two species competition in a periodic environment, J. Math. Biol. 10 (1980) 384-400.
 L. Dong, L. Chen , A periodic predator-prey-chain system with impulsive perturbation, Journal of Computational and Applied Mathematics 223 (2009) 578-584
 K. Zhao, Y. Ye, Four positive periodic solutions to a periodic Lotka- Volterra predatory-prey system with harvesting terms, Nonlinear Anal. Real World Appl. 11 (2010) 2448-2455.
 D. Hu, Z. Zhang, Four positive periodic solutions to a Lotka-Volterra cooperative system with harvesting terms, Nonlinear Anal. Real World Appl. 11 (2010) 1115-1121.
 Y. Kuang, Delay Differential Equations With Applications in Population Dynamics, Academic Press, Inc., 1993.
 R. Gaines, J. Mawhin, Coincidence Degree and Nonlinear Differetial Equitions, Springer Verlag, Berlin, 1977.