Sliding motion and global dynamics of a Filippov fire-blight model with economic thresholds

摘要

AbstractCutting off infected branches has always been an effective method for removing fire-blight infection in an orchard. We introduce a Filippov fire-blight model with a threshold policy: cutting off infected branches and replanting susceptible trees. The dynamics of the proposed piecewise smooth model are described by differential equations with discontinuous right-hand sides. For each susceptible threshold valueST, we investigate the global dynamical behaviour of the Filippov system, including the existence of all the possible equilibria, their stability and sliding-mode dynamics, as we vary the infected threshold levelIT. Our results show that model solutions ultimately approach the equilibrium that lies in the region aboveITor belowITor on展开▼