Hybrid Control Synthesis for Turing Instability and Hopf Bifurcation of Marine Planktonic Ecosystems With Diffusion

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.

Keywords

• Diffusive plankton systems
• Hopf bifurcation
• turing instability
• turing patterns
• hybrid control