Open AccessDynamics of a toxin-mediated aquatic population model with delayed toxic responses
Author(s) -
Yue Ping Dong,
Jian Lu Ren,
Qihua Huang
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020315
Subject(s) - aquatic environment , population , reproduction , aquatic ecosystem , biology , stability (learning theory) , basic reproduction number , ecology , biological system , environmental science , demography , computer science , machine learning , sociology
Traditional mathematical models for studying the effects of environmental toxins on population dynamics usually assume that the toxic effects are immediate. However, the effects of toxins on the reproduction and mortality of aquatic populations can be delayed in reality. In this paper, we propose a new mathematical model with delayed toxic responses for aquatic populations in polluted aquatic environments. The delayed model is analyzed in terms of steady states, stability, and bifurcation. The results show that the delayed effect on the reproduction of aquatic populations does not affect the stability of the interior equilibrium, but the delayed effect on the mortality of aquatic populations can destabilize the interior equilibrium. Numerical results corroborate the theoretical ones are presented.