American Institute of Mathematical Sciences

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

Dynamic behaviour of a periodic competitive system with pulses

Benedetta Lisena 1,

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.
Keywords: asymptotic stability., Lotka-Volterra system, impulsive effect, periodic solution.
Mathematics Subject Classification: 34A3.
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

show all references

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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