×

zbMATH — the first resource for mathematics

Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka-Volterra systems. (English) Zbl 1112.34052
Summary: Sufficient conditions are obtained for the existence and global attractivity of periodic positive solutions of periodic single-species impulsive Lotka-Volterra systems.

MSC:
34K13 Periodic solutions to functional-differential equations
34K45 Functional-differential equations with impulses
92D25 Population dynamics (general)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lakshmikantham, V.; Bainov, D.D.; Simeonov, P.S., Theory of impulsive differential equations, (1989), World Scientific Boston, MA · Zbl 0719.34002
[2] Hale, J.K.; Lunel, S.M.V., Introduction to functional differential equations, (1993), Springer-Verlag Singapore
[3] Kuang, Y., Delay differential equations with application in population dynamics, (1993), Academic Press New York
[4] Györi, I.; Ladas, G., Oscillation theory of delay differential equations with applications, (1991), Clarendon Boston, MA · Zbl 0780.34048
[5] Gopalsamy, K., Stability and oscillation in delay differential equations of population dynamics, (1992), Kluwer Adademic Oxford · Zbl 0752.34039
[6] Erbe, L.H.; Kong, Q.; Zhang, B.G., Oscillation theory for functional differential equations, (1995), Marcel Dekker Dordrecht
[7] Gilpin, M.E.; Ayala, F.J., Global models of growth and competition, (), 3590-3593 · Zbl 0272.92016
[8] Gopalsamy, K.; Kulenovic, M.R.S.; Ladas, G., Environmental periodicity and time delays in a “food limited” population model, J. math. anal. appl., 147, 545-555, (1990) · Zbl 0701.92021
[9] Gopalsamy, K.; Zhang, B.G., On delay differential equation with impulses, J. math. anal. appl., 139, 110-122, (1989) · Zbl 0687.34065
[10] Ballinger, G.; Liu, X., Existence, uniqueness and boundedness results for impulsive delay differential equations, Appl. anal., 74, 71-93, (2000) · Zbl 1031.34081
[11] Anokhin, A.; Berezansky, L.; Braverman, E., Exponential stability of linear delay impulsive differential equations, J. math. anal. appl., 193, 923-941, (1995) · Zbl 0837.34076
[12] Yu, J.S., Explicit conditions for stability of nonlinear scalar delay differential equations with impulses, Nonlinear analysis, 46, 53-67, (2001) · Zbl 0986.34063
[13] Shen, J.H., The nonoscillatory solutions of delay differential equations with impulses, Appl. math. comput., 77, 153-156, (1996) · Zbl 0861.34044
[14] Berezansky, L.; Braverman, E., Oscillation of a linear delay impulsive differential equation, Comm. appl. nonlinear anal., 3, 61-77, (1996) · Zbl 0858.34056
[15] Bainov, D.D.; Stamova, J.M., Existence uniqueness and continuability of solutions of impulsive differential-difference equations, Indian J. pure appl. math., 31, 563-571, (2000) · Zbl 0960.34068
[16] Yan, J.; Zhao, A., Oscillation and stability of linear impulsive delay differential equations, J. math. anal. appl., 227, 187-194, (1998) · Zbl 0917.34060
[17] Tang, X.H.; Zou, X., 3/2-type criteria for global attractivity of Lotka-Volterra competition system without instantaneous negative feedbacks, J. differential equations, 186, 420-439, (2002) · Zbl 1028.34070
[18] Fan, M.; Wang, K.; Jiang, D., Existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with several deviating arguments, Math. biosci., 160, 47-61, (1999) · Zbl 0964.34059
[19] He, X., Stability and delays in a predator-prey system, J. math. anal. appl., 198, 355-370, (1996) · Zbl 0873.34062
[20] He, X., Stability and delays in a predator-prey system II, Dynam. contin. discrete impuls. systems, 7, 177-187, (2000) · Zbl 0952.34061
[21] Xiao, Y.; Wang, W.; Chen, J., Permanence and periodic solution of nonautonomous delay Lotka-Volterra diffusion system, Systems sci. math. sci., 12, 344-349, (1999) · Zbl 0991.34060
[22] Lu, Z., An extension of kamake theorem and periodic Lotka-Volterra systems with diffusion, Appl. anal., 79, 293-300, (2001) · Zbl 1029.35135
[23] Zhang, Y., Global attractivity of Lotka-Volterra systems with infinite delay, Dynam. contin. discrete impuls. systems, 1, 233-244, (1995) · Zbl 0868.45003
[24] Barbalat, I., Systems d’equations differentielles d’oscillations nonlineaires, Rev. roum. math. pures appl., 4, 267-270, (1959) · Zbl 0090.06601
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.