JSEA  Vol.5 No.12 B , December 2012
Periodic Solution of n-Species Gilpin-Ayala Competition System with Impulsive Perturbations
Author(s) Kaihua Wang*, Zhanji Gui
ABSTRACT
The principle aim of this paper is to explore the existence of periodic solution of n-Species Gilpin-Ayala competition system with impulsive perturbations. Sufficient and realistic conditions are obtained by using Mawhin's continuation theorem of the coincidence degree. Further, some numerical simulations show that our model can occur in many forms of complexities including periodic oscillation and chaotic strange attractor.

Cite this paper
K. Wang and Z. Gui, "Periodic Solution of n-Species Gilpin-Ayala Competition System with Impulsive Perturbations," Journal of Software Engineering and Applications, Vol. 5 No. 12, 2012, pp. 26-29. doi: 10.4236/jsea.2012.512B006.
References
[1]   Ayala F J, Gilpin M E and Eherenfeld J G “Competition between species: Theoretical models and experimental tests,” Theoret. Popul. Biol. 4 (1973) 331-56.

[2]   Gilpin M E and Ayala F J “Global models of growth and competition,” Proc. Natl. Acad. Sci. USA. 70 (1973) 3590-93.

[3]   Liao X X and Li J “Stability in Gilpin-Ayala competition models with diffusion,” Non-linear Anal. 28 19971751-58

[4]   Ahmad S and Lazer A C “Average conditions for global asymptotic stability in a nonautonomous Lotka-Volterra system,” Nonlinear Anal. 40 (2000) 37-49.

[5]   Chen F D “Average condi-tions for permanence and extinction in nonautonomous Gilpin-Ayala competition model,” Nonlinear Anal. 4 (2006) 895-915.

[6]   Xia Y H, Han M A and Huang Z K “Global attractivity of an almost periodic N-Species nonlinear ecological competitive model,” J. Math. Anal. Appl. 337 (2008) 144-168.

[7]   Wang Q, Ding M M, Wang Z J and Zhang H Y “Existence and attractivity of a periodic solution for an N-species Gilpin-Ayala impul-sive competition system” Nonlinear Ana: Real World Applications 11 (2010) 2675-85

[8]   Gaines R E and Mawhin J L “Coincidence degree and nonlinear diferen-tial equations ” Springer-Verlag, Berlin, 1977.

[9]   Zhang J and Gui Z J “Periodic solutions of nonautonomous cellular neural networks with impulses and delays,” Nonlinear Analysis: Real World Applica-tions. 10 (2009) 1891-1903.

 
 
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