Theoretical exploration and controller design of bifurcation in a plankton population dynamical system accompanying delay
Changjin Xu, Wei Ou, Qingyi Cui, Yicheng Pang, Maoxin Liao, Jianwei Shen, Muhammad Zafarullah Baber, C. Maharajan, Uttam Ghosh
Abstract
Formulating suitable dynamical models to describe the interplay of different chemical substance in biology and chemistry is a very interesting topic. In this article, we set up a new plankton population dynamical system accompanying delay. Taking advantage of fixed point theorem and appropriate function, we derive the criteria on existence and uniqueness, boundedness of the solutions of the established plankton population dynamical system. By applying Hopf bifurcation and stability theorem of delayed dynamical system, we analyze the emergence of Hopf bifurcation and stability trait of the established plankton population dynamical system. Novel delay-independent criteria guaranteeing the emergence of Hopf bifurcation and stability of the system are derived. By virtue of two different controllers, we have effectively controlled the time of occurrence of Hopf bifurcation and stability domain of the established system. The influence of time delay on Hopf bifurcation and stability of the system is shown. The study shows that when the delay crosses a critical value, then Hopf bifurcations of the established plankton population dynamical system and its controlled systems arise. Numerical experiment outcomes are included to support the derived main fruits. The derived results of this article are completely new and have important theoretical value in balancing and controlling the concentrations of distinct chemical substances.