Impulsive state feedback control of the rhizosphere microbial degradation in the wetland plant (Q1723426)

Summary: The rhizosphere microbe plays an important role in removing the pollutant generated from industrial and agricultural production. To investigate the dynamics of the microbial degradation, a nonlinear mathematical model of the rhizosphere microbial degradation is proposed based on impulsive state feedback control. The sufficient conditions for existence of the positive order-1 or order-2 periodic solution are obtained by using the geometrical theory of the semicontinuous dynamical system. We show the impulsive control system tends to an order-1 periodic solution or order-2 periodic solution if the control measures are achieved during the process of the microbial degradation. Furthermore, mathematical results are justified by some numerical simulations.