Turing Instability and Hopf Bifurcation Analysis for A Hybrid Control Biological System with One-Dimensional Diffusion

The optimal control of the dynamical behavior of reaction-diffusion systems has been rarely studied. In this paper, we put forward a novel one-dimensional reaction-diffusion marine planktonic biological system depicted by partial differential equations, and propose a class of hybrid control optimization algorithms for this system. In the analysis, the local stability of the system is determined firstly. Then, the condition of appearances of Turing patterns induced by diffusion and the criterion of Hopf bifurcation induced by time delay are obtained, respectively. Next, select the appropriate controller parameters to optimize the dynamic behavior of the system. Finally, several numerical simulations are utilized to verify the correctness of the theoretical results.