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Dynamics for a tritrophic impulsive periodic plankton–fish system with diffusion in lakes
Author(s) -
Liu Guodong,
Meng Xinzhu,
Liu Siyu
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6938
Subject(s) - mathematics , reaction–diffusion system , diffusion , plankton , comparison theorem , fish <actinopterygii> , control theory (sociology) , stability (learning theory) , functional response , fixed point , dynamics (music) , ecology , mathematical analysis , predation , computer science , fishery , biology , physics , thermodynamics , acoustics , control (management) , artificial intelligence , machine learning , predator
Impulsive reaction–diffusion system is a novel assemblage of tools for better understanding ecological dynamics. This paper is devoted to mathematical and biological analysis of an impulsive tritrophic periodic plankton–fish system with diffusion and Beddington–DeAngelis functional response in lakes. On the basis of comparison theory and method of upper and lower solution, we have rigorously analyzed ultimate boundedness and permanence of the reaction–diffusion system under impulsive effects. Significantly, the existence and globally asymptotic stability of a unique positive periodic solution are verified by Brouwer's fixed point theorem and auxiliary function method. Additionally, two particular scenarios are chosen to illustrate our results. It is found that impulsive effects can influence lake ecological dynamics and regulate lake biological structure.