Bifurcation Analysis And Optimal Control Of The Crowley Martin Phytoplankton-Zooplankton Model That Considers The Impact Of Nanoparticles

Lakshmi N.Sridhar

Chemical Engineering Department, University of Puerto Rico, Mayaguez, PR 00682, (USA)

PAGE NO: 54-60

ABSTRACT – DOI: https://dx.doi.org/10.47204/EMSR.5.1.2023.054-060

Bifurcation analysis and multiobjective nonlinear model predictive control calculations are performed on the Crowley Martin phytoplankton-zooplankton model studied by Kumar and Pramanick (2022). The bifurcation analysis confirms the existence of the oscillation causing Hopf bifurcations while the multiobjective nonlinear model predictive control (MNLMPC) calculations demonstrate the existence of spikes in the control profile. Bifurcation analysis was performed using the MATLAB software MATCONT while the multiobjective nonlinear model predictive control was performed by using the optimization language PYOMO. An activation factor involving the tanh function is shown to eliminate both the spikes and the Hopf bifurcations.