Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE DYNAMIC OF TWO-SPECIES IMPULSIVE DELAY GILPIN-AYALA COMPETITION SYSTEM WITH PERIODIC COEFFICIENTS

  • Zhang, Shuwen (College of Science, Jimei University) ;
  • Tan, Dejun (Collegeof education of Teacher, Jimei University)
  • Received : 2010.08.23
  • Accepted : 2011.04.15
  • Published : 2011.09.30
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Abstract

In this paper, we consider two-species periodic Gilpin-Ayala competition system with delay and impulsive effect. By using some analysis methods, sufficient conditions for the permanence of the system are derived. Further, we give the conditions of the existence and global asymptotic stable of positive periodic solution.

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References

  1. D.Bainov, and P.Simeonor, Impulsive differential equations:periodic solutions and applica- tion, Pitman Monographs and Surrys in Pure and Applied Mathematics, 1993.
  2. G.R. Jiang and Q.G Yang, Bifurcation analysis in an SIR epidemic model with birth pulse and pulse vaccination. Applied mathematics and computation, Applied mathematics and computation 215 (2009), 1035-1046. https://doi.org/10.1016/j.amc.2009.06.032
  3. G.Ballinger and X.Liu, Permanence of population growth models with impulsive effects,, Math.Comput.Model 26 (1997), 59-72.
  4. J. Hou, Z.D. Teng and S.J. Gao, Permanence and global stablity for nonautonomous Nspecies Lotka-Valterra competitive system with impulses, Nonlinear Analysis: Real world Applications. 11 (2010), 1882-1896. https://doi.org/10.1016/j.nonrwa.2009.04.012
  5. A.Lakmeche and O.Arin, Bifurcation of non-trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment, Dynamics of continuous, Discrete Impulsive system. 7 (2000), 265-287.
  6. H.K.Beak, Qualitative analysis of Beddington-DeAngelis type impulsive predator-prey models, Nonlinear Analysis: Real world Applications. 11 (2010), 1312-1322. https://doi.org/10.1016/j.nonrwa.2009.02.021
  7. M.G.Roberts and R.R.Kao, The dynamics of an infectious disease in a population with birth pulsed, Math.Biosci. 149 (1998), 23-36. https://doi.org/10.1016/S0025-5564(97)10016-5
  8. S.Y.Tany and L.S.Chen, Density-dependent birth rate,birth pulse and their population dynamic consequences, J.Math.Biol. 44 (2002), 185-199. https://doi.org/10.1007/s002850100121
  9. X.N.Liu and L.S. Chen,, Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator, Chaos, Solitons Fractals. 16 (2003), 311-320. https://doi.org/10.1016/S0960-0779(02)00408-3
  10. G.Balling and X.Liu, Existence,uniqueness and boundedness results for impulsive delay differential equations, J.Math.Appl.Anal. 74 (2000), 71-93.
  11. J.S. Yu, Explicit conditions for stablility of nonlinear scalar delay differential equations with impulsive, Nonlinear Analysis 46 (2001), 53-67. https://doi.org/10.1016/S0362-546X(99)00445-9
  12. J.H.Shen, The nonoscillatory solutions of delay differential equations with impulses, Appl.Math.Comput.77 (1996), 153-156. https://doi.org/10.1016/S0096-3003(95)00198-0
  13. J.Yan and A.Zhao, Oscillation and stability of linear impulsive delay differential equation, J.Math.Anal.Appl227(1998), 187-194. https://doi.org/10.1006/jmaa.1998.6093
  14. M.E.Gilpin and F.J.Ayala, Global models of growth and competition, Proc Nat Acad Sci USA70(1973), 3590-4003. https://doi.org/10.1073/pnas.70.12.3590
  15. M.Fan and K.Wang, Global periodic solution of a generalized n-species Gilpin-Ayala com- petition model, Comput.Math. Appl.40(2000), 1141-1151. https://doi.org/10.1016/S0898-1221(00)00228-5
  16. R.E.Gaines and J.L.Lazer, Coincidence degree and nonlinear differential equations Berlin:Springer Verlag;1977.
  17. M.X He, Z. Li and F.D Chen, Permanence, extinction and global attractivity of the periodic Gilpin-Ayala competition system with impulses, Nonlinear analysis: Real world applications. 11(2010), 1537-1551. https://doi.org/10.1016/j.nonrwa.2009.03.007