×

Permanence of a general periodic single-species system with periodic impulsive perturbations. (English) Zbl 1116.92052

Summary: Sufficient conditions for permanence of a general periodic single-species system with periodic impulsive perturbations are obtained via comparison theory of impulsive differential equations. An application is given to a periodic impulsive logistic system.

MSC:

92D25 Population dynamics (general)
34A37 Ordinary differential equations with impulses
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D99 Stability theory for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] D.D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications. Longman, England, 1993. · Zbl 0815.34001
[2] E. Funasaki and M. Kot, Invasion and chaos in a periodically pulsed mass-action chemostat. Theor. Popul. Biol.,44 (1993), 203–224. · Zbl 0782.92020
[3] S. Gao and L. Chen, The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses. Chaos, Solitons & Fractals,24 (2005), 1013–1023. · Zbl 1061.92059
[4] A. Lakmeche, O. Arino, Birfurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment. Dynam. Contin. Discrete Impuls.,7 (2000), 265–287. · Zbl 1011.34031
[5] V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations. World Scientific, Singapore, 1989. · Zbl 0719.34002
[6] W. Li and H. Huo, Global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics, J. Comput. Appl. Math.,174 (2005), 227–238. · Zbl 1070.34089
[7] W. Li and H. Huo, Existence and global attractivity of positive periodic solutions of functional differential equations with impulses. Nonlinear Analysis,59 (2004), 857–877. · Zbl 1061.34059
[8] B. Liu, Y. Zhang and L. Chen, The dynamical behaviors of a Lotka-Volterra predator-prey model concerning integrated pest management. Nonlinear Anal. Real World Appl.,6 (2005), 227–243. · Zbl 1082.34039
[9] X. Liu and L. Chen, Global dynamics of the periodic logistic system with periodic impulsive perturbations. J. Math. Anal. Appl.,289 (2004), 279–291. · Zbl 1054.34015
[10] X. Liu and L. Chen, Global attractivity of positive periodic solutions for nonlinear impulsive systems. Nonlinear Analysis,65 (2006), 1843–1857. · Zbl 1111.34010
[11] M.G. Roberts and R.R. Kao, The dynamics of an infectious disease in a population with birth pulses. Math. Biosci.,149 (1998), 23–36. · Zbl 0928.92027
[12] B. Shulgin, L. Stone and Z. Agur, Pulse vaccination strategy in the SIR epidemic model. Bull. Math. Biol.,60 (1998), 1123–1148. · Zbl 0941.92026
[13] S. Tang and L. Chen, Density-dependent birth rate, birth pulses and their population dynamic consequences. J. Math. Biol.,44 (2002), 185–199. · Zbl 0990.92033
[14] S. Tang and L. Chen, Global attractivity in a ”food-limited” population model with impulsive effects. J. Math. Anal. Appl.,292 (2004), 211–221. · Zbl 1062.34055
[15] J. Yan, A. Zhao and J. J. Nieto, Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka–Volterra systems. Math. Comput. Model.,40 (2004), 509–518. · Zbl 1112.34052
[16] B. Zhang and Y. Liu, Global attractivity for certain impulsive delay differential equations. Nonlinear Analysis,52 (2003), 725–736. · Zbl 1027.34086
[17] W. Zhu, D. Xu and Z. Yang, Global exponential stability of impulsive delay difference equation. Appl. Math. Comput.,181 (2006), 65–72. · Zbl 1148.39304
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.