Mathematical Analysis of Time Delayed Model of Phytoplankton and Zooplankton Species
摘要
The phytoplankton and zooplankton are two essential components of aquatic ecosystem. Through the analysis conducted in this paper, a time delayed model of phytoplankton and zooplankton has been framed mathematically and analyzed to elucidate the synergistic relationship between two populations in aquatic habitat. The system has been explored for significant features like positivity and boundededness of solution. The emergence of various steady points accompanied by their steadiness results has been investigated. The presence of Hopf bifurcation has been indicated by carrying out a thorough analysis of the related characteristic equation. It has been noticed that in absence of delay, the parameter “r” and “ \(\beta \) ” contributes significantly toward the stability of the system, whereas the periodic oscillations in two species appear in relation to parameter “ \(\tau \) ”. To demonstrate the validity of analytical results, simulation-based analysis is performed with the help of MATLAB and MATCONT.