Existence of Multiple Positive Periodic Solutions to n Species Nonautonomous Lotka-Volterra Cooperative Systems with Harvesting Terms
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32920
Existence of Multiple Positive Periodic Solutions to n Species Nonautonomous Lotka-Volterra Cooperative Systems with Harvesting Terms

Authors: Kaihong Zhao

Abstract:

In this paper, the existence of 2n positive periodic solutions for n species non-autonomous Lotka-Volterra cooperative systems with harvesting terms is established by using Mawhin-s continuation theorem of coincidence degree theory and matrix inequality. An example is given to illustrate the effectiveness of our results.

Keywords: Multiple positive periodic solutions, Nonautonomous Lotka-Volterra cooperative system, Coincidence degree, Harvesting term.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079624

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1322

References:


[1] Z. Ma, Mathematical modelling and studing on species ecology, Education Press, Hefei, 1996 (in Chinese).
[2] Horst R. Thieme, Mathematics in Population Biology, In: Princeton Syries in Theoretial and Computational Biology, Princeton University Press, Princeton, NJ, 2003.
[3] R. Gaines, J. Mawhin, Coincidence Degree and Nonlinear Differetial Equitions, Springer Verlag, Berlin, 1977.
[4] Y. Chen, Multiple periodic solutions of delayed predator-prey systems with type IV functional responses, Nonlinear Anal. Real World Appl. 5(2004) 45-53.
[5] Q. Wang, B. Dai, Y. Chen, Multiple periodic solutions of an impulsive predator-prey model with Holling-type IV functional response, Math. Comput. Modelling 49 (2009) 1829-1836.
[6] 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.
[7] 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.
[8] K. Zhao, Y. Li, Four positive periodic solutions to two species parasitical system with harvesting terms, Computers and Mathematics with Applications. 59 (2010) 2703-2710.
[9] Z. Li, K. Zhao, Y. Li, Multiple positive periodic solutions for a non-autonomous stage-structured predatory-prey system with harvesting terms, Commun Nonlinear Sci Numer Simulat. 15 (2010) 2140-2148.
[10] Y. Li, K. Zhao, Y. Ye, Multiple positive periodic solutions of n species delay competition systems with harvesting terms, Nonlinear Anal. Real World Appl. 12 (2011) 1013-1022.
[11] X. Liao, Methods and Applications of Stable Theory , Central China Normal University Press, Wuhan, 2001 (in Chinese).
[12] Y. Li, Y. Kuang, Periodic solutions of periodic delay Lotka-Volterra equations and systems, J. Math. Anal. Appl. 255 (2001) 260-280.