2n Positive Periodic Solutions to n Species Non-autonomous Lotka-Volterra Competition Systems with Harvesting Terms

By using Mawhin-s continuation theorem of coincidence degree theory, we establish the existence of 2n positive periodic solutions for n species non-autonomous Lotka-Volterra competition systems with harvesting terms. An example is given to illustrate the effectiveness of our results.

• Yongkun Li
• Kaihong Zhao

• Positive periodic solutions
• Lotka-Volterra competition system
• coincidence degree
• harvesting term.

[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] Y. Li, Y. Kuang, Periodic solutions of periodic delay Lotka-Volterra
equations and systems, J. Math. Anal. Appl. 255 (2001) 260-280.