Bifurcation analysis of phytoplankton-fish model through parametric control by fish mortality rate and food transfer efficiency

Kalyan Das, V. Madhusudanan, M. N. Srinivas, Md Humayun Kabir, Md Osman Gani, Sardar M. N. Islam


An Algae-zooplankton fish model is studied in this article. First the proposed model is evaluated for positive invariance and boundedness. Then,the Routh-Hurwitz parameters and the Lyapunov function are used to determine the presence of a positive interior steady state and the criteria for plankton model stability (both local and global). Taylor’s sequence is also used to discuss Hopf bifurcation and the stability of bifurcated periodic solutions. The model’s bifurcation analysis reveals that Hopf-bifurcation can occur when mortality rate and food transfer efficiency are used as bifurcation parameters. Finally, we use numerical simulation to validate the analytical results.


Phytoplankton; Zooplankton; Stability; Lyapunov Exponent; Hopf-bifurcation

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