# American Institute of Mathematical Sciences

June  2013, 6(3): 723-729. doi: 10.3934/dcdss.2013.6.723

## Dynamic behaviour of a periodic competitive system with pulses

 1 Dipartimento di Matematica, Universitá degli studi di Bari, 70125 Bari, Italy

Received  March 2010 Revised  December 2010 Published  December 2012

In this article we consider an $n$-dimensional competitive Lotka-Volterra system with periodic coefficients and impulses. We provide sufficient conditions for the existence and global attractivity of a positive periodic solution.
Citation: Benedetta Lisena. Dynamic behaviour of a periodic competitive system with pulses. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 723-729. doi: 10.3934/dcdss.2013.6.723
##### References:
 [1] S. Ahmad and I. M.Stamova, Asymptotic stability of an N-dimensional impulsive competitive system,, Nonlinear Anal. Real World Appl., 8 (2007), 654. doi: 10.1016/j.nonrwa.2006.02.004. Google Scholar [2] S. Ahmad and A. C. Lazer, Average growth and extinction in a competitive Lotka-Volterra system,, Nonlinear Anal., 62 (2005), 545. doi: 10.1016/j.na.2005.03.069. Google Scholar [3] S. Ahmad and A. C. Lazer, Average conditions for global asymptotic stability in a nonautonomous Lotka-Volterra system,, Nonlinear Anal., 40 (2000), 37. doi: 10.1016/S0362-546X(00)85003-8. Google Scholar [4] D. D. Bainov and P. S. Simeonov, "Systems with Impulse Effect,", Elles Horwood Limited, (1989). Google Scholar [5] D. D. Bainov and P. S. Simeonov, "Impulsive Differential Equations: Periodic Solutions and Applications,", Longmann Scientific and Technical, (1993). Google Scholar [6] B. Lisena, Stability and periodicity in competitive systems with impulses,, Mediterr. J. Math., 6 (2009), 291. doi: 10.1007/s00009-009-0009-4. Google Scholar [7] B. Lisena, Coexistence and extinction in competitive systems with impulses,, Dyn. Contin. Discrete Impuls. Syst. Ser. A, 17 (2010), 619. Google Scholar [8] B. Lisena, Global stability in periodic competitive systems,, Nonlinear Anal. Real World Appl., 5 (2004), 613. doi: 10.1016/j.nonrwa.2004.01.002. Google Scholar [9] B. Liu, Z. Teng and W. Liu, Dynamic behaviors of the periodic Lotka-Volterra competing systems with impulsive perturbations,, Chaos Solitons Fractals, 31 (2007), 356. doi: 10.1016/j.chaos.2005.09.059. Google Scholar [10] I. Stamova, "Stability Analysis of Impulsive Functional Differential Equations,", Walter de Gruyter, (2009). doi: 10.1515/9783110221824. Google Scholar [11] J. Zhen, M. Han and G. Li, The persistence in a Lotka-Volterra competition system with impulsive,, Chaos Solitons Fractals, 24 (2005), 1105. doi: 10.1016/j.chaos.2004.09.065. Google Scholar

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##### References:
 [1] S. Ahmad and I. M.Stamova, Asymptotic stability of an N-dimensional impulsive competitive system,, Nonlinear Anal. Real World Appl., 8 (2007), 654. doi: 10.1016/j.nonrwa.2006.02.004. Google Scholar [2] S. Ahmad and A. C. Lazer, Average growth and extinction in a competitive Lotka-Volterra system,, Nonlinear Anal., 62 (2005), 545. doi: 10.1016/j.na.2005.03.069. Google Scholar [3] S. Ahmad and A. C. Lazer, Average conditions for global asymptotic stability in a nonautonomous Lotka-Volterra system,, Nonlinear Anal., 40 (2000), 37. doi: 10.1016/S0362-546X(00)85003-8. Google Scholar [4] D. D. Bainov and P. S. Simeonov, "Systems with Impulse Effect,", Elles Horwood Limited, (1989). Google Scholar [5] D. D. Bainov and P. S. Simeonov, "Impulsive Differential Equations: Periodic Solutions and Applications,", Longmann Scientific and Technical, (1993). Google Scholar [6] B. Lisena, Stability and periodicity in competitive systems with impulses,, Mediterr. J. Math., 6 (2009), 291. doi: 10.1007/s00009-009-0009-4. Google Scholar [7] B. Lisena, Coexistence and extinction in competitive systems with impulses,, Dyn. Contin. Discrete Impuls. Syst. Ser. A, 17 (2010), 619. Google Scholar [8] B. Lisena, Global stability in periodic competitive systems,, Nonlinear Anal. Real World Appl., 5 (2004), 613. doi: 10.1016/j.nonrwa.2004.01.002. Google Scholar [9] B. Liu, Z. Teng and W. Liu, Dynamic behaviors of the periodic Lotka-Volterra competing systems with impulsive perturbations,, Chaos Solitons Fractals, 31 (2007), 356. doi: 10.1016/j.chaos.2005.09.059. Google Scholar [10] I. Stamova, "Stability Analysis of Impulsive Functional Differential Equations,", Walter de Gruyter, (2009). doi: 10.1515/9783110221824. Google Scholar [11] J. Zhen, M. Han and G. Li, The persistence in a Lotka-Volterra competition system with impulsive,, Chaos Solitons Fractals, 24 (2005), 1105. doi: 10.1016/j.chaos.2004.09.065. Google Scholar
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