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Dynamics of an impulsive model of plankton allelopathy with delays

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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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Acknowledgements

This work was supported by Natural Science Foundation of Fujian Province (2015J05006), the foundation of Education Department of Fujian Province (JAT160063).

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Authors and Affiliations

  1. Mathematics Research Center & College of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350117, People’s Republic of China

    Mengxin He

  2. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350116, Fujian, People’s Republic of China

    Mengxin He, Zhong Li & Fengde Chen

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  1. Mengxin He
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  2. Zhong Li
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Correspondence to Mengxin He.

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He, M., Li, Z. & Chen, F. Dynamics of an impulsive model of plankton allelopathy with delays. J. Appl. Math. Comput. 55, 749–762 (2017). https://doi.org/10.1007/s12190-016-1069-9

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  • DOI: https://doi.org/10.1007/s12190-016-1069-9

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