Dynamical analysis in a piecewise smooth predator-prey model with predator harvesting

The aim of this paper is to study the dynamical behaviors of a piecewise smooth predator-prey model with predator harvesting.We consider a harvesting strategy that allows constant catches if the population size is above a certain threshold value(to obtain predictable yield)and no catches if the population size is below the threshold(to protect the population).It is shown that boundary equilibrium bifurcation and sliding grazing bifurcation can happen as the threshold value varies.We provide analytical analysis to prove the existence of sliding limit cycles and sliding homoclinic cycles,the coexistence of them with standard limit cycles.Some numerical simulations are given to demonstrate ourresults.