Releasing amount of natural enemy generally depends on its population data, while impulsive releasing natural enemy usually brings about a time delay after the data is observed in the practical pest management. Therefore, it is very important for pest managers to assess the impact of the time delay in pest management. In this paper, we construct a pest-natural enemy model with time delay in impulsive releasing natural enemy. We prove that the pest-free periodic solution of model $(2.1)$ is globally attractive with $\eta \tau<\frac{\zeta y^{\ast}(1-e^{-\lambda \tau})}{\lambda}$. We also prove that model $(2.1)$ is permanent with $\eta \tau>\frac{\zeta y^{\ast}(1-e^{-\lambda \tau})}{\lambda}$.... More >

This paper deals with continuous piecewise linear differential systems with three zones separated by two parallel straight lines (for short, CPWL3). The number of limit cycles of CPWL3 systems with two degenerate subsystems is not clear. In the paper, we provide a complete study on the maximum number of limit cycles by geometric techniques when the continuous piecewise linear systems with three zones have two degenerate subsystems. During our analysis, we also detect some bifurcation phenomena, such as boundary equilibrium bifurcation, scabbard bifurcation, grazing bifurcation, heteroclinic bifurcation and Hopf bifurcation. More >

Presents the introductory editorial for this issue of the publication. More >