Hybrid Control Synthesis for Turing Instability and Hopf Bifurcation of Marine Planktonic Ecosystems With Diffusion
Yunxiang Lu, Min Xiao, Jinling Liang, Jie Ding, Ying Zhou, Youhong Wan, Chunxia Fan
Abstract
Great progress has been made in bifurcation control of systems described by ordinary differential equations. However, the control of Hopf bifurcation and Turing patterns is seldom reported in reaction-diffusion systems, which is formed by partial differential equations. In this paper, a hybrid control synthesis combining state feedback is firstly devised in the reaction-diffusion marine planktonic ecosystem. The Turing instability condition and Hopf bifurcation criterion are derived through carrying out the eigenvalue analysis of the controlled system. The numerical simulations show that the hybrid control strategy can not only suppress the formation of Turing patterns, but also delay or advance the Hopf bifurcation point. Therefore, the desired spatial dynamics behaviors can be generated by manipulate the control gain parameters, so as to achieve the purpose of maintaining the marine ecological balance.