Multiple Positive Periodic Solutions of a Competitor-Competitor-Mutualist Lotka-Volterra System with Harvesting Terms
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32807
Multiple Positive Periodic Solutions of a Competitor-Competitor-Mutualist Lotka-Volterra System with Harvesting Terms

Authors: Yongkun Li, Erliang Xu

Abstract:

In this paper, by using Mawhin-s continuation theorem of coincidence degree theory, we establish the existence of multiple positive periodic solutions of a competitor-competitor-mutualist Lotka-Volterra system with harvesting terms. Finally, an example is given to illustrate our results.

Keywords: Positive periodic solutions, competitor-competitor mutualist Lotka-Volterra systems, coincidence degree, harvesting term.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078885

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1311

References:


[1] M. Gyllenberg, P. Yan, Y. Wang, Limit cycles for competitor-competitormutualist Lotka-Volterra systems, Physica D 221 (2006) 135-145.
[2] C.V. Pao, The global attractor of a competitor-competitor-mutualist reaction-diffusion system with time delays, Nonlinear Anal. 67 (2007) 2623-2631.
[3] W.Y. Chen, R. Peng, Stationary patterns created by cross-diffusion for the competitor- competitor-mutualist model, J. Math. Anal. Appl. 291 (2004) 550-564.
[4] S. Fu, Persistence in a periodic competitor-competitor-mutualist diffusion system, J. Math. Anal. Appl. 263, 234-245 (2001).
[5] X. Lv, P. Yan, S. Lu, Existence and global attractivity of positive periodic solutions of competitor-competitor-mutualist Lotka-Volterra systems with deviating arguments, Math. Comput. Modelling 51 (2010) 823-832.
[6] M. Li, Z. Lin, J.H. Liu, Coexistence in a competitor-competitor-mutualist model, Appl. Math. Modelling, in press, doi:10.1016/j.apm.2010.02.029
[7] Z. Ma, Mathematical Modelling and Studing on Species Ecology, Education Press, Hefei, 1996, (in Chinese).
[8] H.R. Thieme, Mathematics in population biology, in: Princeton Syries in Theoretial and Computational Biology, Princeton University Press, Princeton, NJ, 2003.
[9] R. Gaines, J. Mawhin, Coincidence Degree and Nonlinear Differetial Equitions, Springer Verlag, Berlin, 1977.
[10] 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.
[11] 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.
[12] K.H. Zhao, Y. Ye, Four positive periodic solutions to a periodic Lotka- Volterra predatory-prey system with harvesting terms, Nonlinear Anal. Real World Appl. in press, doi:10.1016/j.nonrwa.2009.08.001.
[13] K.H. Zhao, Y.K. Li, Four positive periodic solutions to two species parasitical system with harvesting terms, Comput. Math. Appl. 59 (2010) 2703-2710.