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Stability and bifurcation analysis of a nutrient‐phytoplankton model with time delay
Author(s) -
Guo Qing,
Dai Chuanjun,
Yu Hengguo,
Liu He,
Sun Xiuxiu,
Li Jianbing,
Zhao Min
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.6098
Subject(s) - hopf bifurcation , mathematics , nonlinear system , bifurcation , stability (learning theory) , phytoplankton , control theory (sociology) , instability , exponential stability , nutrient , mechanics , physics , computer science , ecology , biology , control (management) , quantum mechanics , machine learning , artificial intelligence
We proposed a nutrient‐phytoplankton interaction model with a discrete and distributed time delay to provide a better understanding of phytoplankton growth dynamics and nutrient‐phytoplankton oscillations induced by delay. Standard linear analysis indicated that delay can induce instability of a positive equilibrium via Hopf bifurcation. We derived the conditions guaranteeing the existence of Hopf bifurcation and tracked its direction and the stability of the bifurcating periodic solutions. We also obtained the sufficient conditions for the global asymptotic stability of the unique positive steady state. Numerical analysis in the fully nonlinear regime showed that the stability of the positive equilibrium is sensitive to changes in delay values under select conditions. Numerical results were consistent with results predicted by linear analysis.