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Journal of Applied Mathematics and Computing
Published in: Journal of Applied Mathematics and Computing 1-2/2017

18-01-2017 | Original Research

Dynamics of an impulsive model of plankton allelopathy with delays

Authors: Mengxin He, Zhong Li, Fengde Chen

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2017

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Abstract

In this paper, we consider an impulsive model of plankton allelopathy with delays. By applying the comparison theorem and constructing some suitable Lyapunov functional, we discuss the permanence and global attractivity of the system. Our result generalizes the corresponding one of Abbas et al. (Nonlinear Dyn 67: 203–214, 2012). We also obtain sufficient conditions ensuring the existence of a unique strictly positive almost periodic solution based on almost periodic functional hull theory of the impulsive differential equations. For the system without delays, our results weaken those of He et al. (Nonlinear Anal 11: 2296–2301, 2010).
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Literature
1.
Smith, M.J.: Models in Ecology. Cambridge University Press, Cambridge (1974)MATH
2.
Chattopadhyay, J.: Effect of toxic substances on a two-species competitive system. Ecol. Model. 84, 287–289 (1996)CrossRef
3.
Chen, F.D., Li, Z., Chen, X.X., Laitochov, J.: Dynamic behaviors of a delay differential equation model of plankton allelopathy. J. Comput. Appl. Math. 206(2), 733–754 (2007)MathSciNetCrossRefMATH
4.
Samanta, G.P.: A two-species competitive system under the influence of toxic substances. Appl. Math. Comput. 216, 291–299 (2010)MathSciNetMATH
5.
Li, Z., Chen, F.D.: Extinction in two dimensional nonautonomous Lotka–Volterra systems with the effect of toxic substances. Appl. Math. Comput. 182, 684–690 (2006)MathSciNetMATH
6.
Mukhopadhyay, A., Chattopadhyay, J., Tapaswi, P.K.: A delay differential equations model of plankton allelopathy. Math. Biosci. 149, 167–189 (1998)MathSciNetCrossRefMATH
7.
Li, Z., Chen, F.D.: Extinction in periodic competitive stage-structured Lotka–Volterra model with the effects of toxic substances. J. Comput. Appl. Math. 231, 143–153 (2009)MathSciNetCrossRefMATH
8.
Abbas, S., Sen, M., Banerjee, M.: Almost periodic solutionof a non-autonomous model of phytoplankton allelopathy. Nonlinear Dyn. 67, 203–214 (2012)CrossRefMATH
9.
Li, Z., Chen, F.D., He, M.X.: Asymptotic behavior of reaction-diffusion model of plankton allelopathy with nonlocal delays. Nonlinear Anal. 12, 1748–1758 (2011)MathSciNetCrossRefMATH
10.
Kar, T.K., Chaudhuri, K.S.: On non-selective harvesting of two competing fish species in the presence of toxicity. Ecol. Model. 161, 125–137 (2003)CrossRef
11.
Li, Z., Chen, F.D., He, M.X.: Global stability of a delay differential equations model of plankton allelopathy. Appl. Math. Comput. 218, 7155–7163 (2012)MathSciNetMATH
12.
He, M.X., Chen, F.D., Li, Z.: Almost periodic solution of an impulsive differential equation model of plankton allelopathy. Nonlinear Anal. 11, 2296–2301 (2010)MathSciNetCrossRefMATH
13.
Chen, L.J., Sun, J.T., Chen, F.D., Zhao, L.: Extinction in a Lotka–Volterra competitive system with impulse and the effect of toxic substances. Appl. Math. Model. 40, 1–10 (2015)
14.
Liu, Z.J., Hui, J., Wu, J.H.: Permanence and partial extinction in an impulsive delay competitive system with the effect of toxic substances. J. Math. Chem. 46, 1213–1231 (2009)MathSciNetCrossRefMATH
15.
Jia, J.G., Wang, M.S., Li, M.L.: Periodic solutions for impulsive delay differential equations in the control model of plankton allelopathy. Chaos Solitons Fractals 32, 962–968 (2007)MathSciNetCrossRefMATH
16.
Liu, Z.J., Wu, J.H., Chen, Y.P., Haque, M.: Impulsive perturbations in a periodic delay differential equation model of plankton allelopathy. Nonlinear Anal. 11, 432–445 (2010)MathSciNetCrossRefMATH
17.
Samoilenko, A.M., Perestyuk, N.A.: Impulsive Differential Equations. World Scientific, Singapore (1995)
18.
Stamov, G.T.: Almost Periodic Solutions of Impulsive Differential Equations. Lecture Notes in Mathematics (2012)
19.
Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
20.
He, M.X., Chen, F.D., Li, Zhong: Permanence and global attractivity of an impulsive delay Logistic model. Appl. Math. Lett. 62, 92–100 (2016)MathSciNetCrossRefMATH
21.
Hou, J., Teng, Z.D., Gao, S.J.: Permanence and global stability for nonautonomous \(N\)-species Lotka–Volterea competitive system with impulses. Nonlinear Anal. 11, 1882–1896 (2010)CrossRefMATH
22.
Chen, F.D., Li, Z., Huang, Y.J.: Note on the permanence of a competitive system with infinite delay and feedback controls. Nonlinear Anal. 8(2), 680–687 (2007)MathSciNetCrossRefMATH
23.
Halanay, A., Wexler, D.: Qualitative Theory of Systems with impulses. Nauka, Moscow (1971)
24.
Metadata
Title
Dynamics of an impulsive model of plankton allelopathy with delays
Authors
Mengxin He
Zhong Li
Fengde Chen
Publication date
18-01-2017
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 1-2/2017
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-016-1069-9

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