Bifurcations and dynamics of a plant disease system under non-smooth control strategy

Mathematical models and analyses can assist in designing the control strategies to prevent the spread of infectious disease. The present paper investigates the bifurcations and dynamics of a plant disease system under non-smooth control strategy. The generalized Lyapunov approach is employed to perform the analysis of the plant disease model with non-smooth control. It is found that the controlled disease system can have three types of equilibria. The globally asymptotically attractor for each of three types of equilibria is determined by constructing Lyapunov functions and using Green's Theorem. It is shown that the disease system can exhibit rich dynamic behaviors including globally stable equilibrium, stable pseudo-equilibrium and sliding mode bifurcations. The solution of the disease system can converge to the disease-free equilibrium, endemic equilibrium or sliding equilibrium on discontinuous surfaces. Biological implications of the obtained results are discussed for implementing the control strategies to the infectious plant diseases.