Sliding dynamics of a Filippov ecological system with nonlinear threshold control and pest resistance

Abstract

By applying the integrated pest management strategy to address pest control problems, Filippov pest-natural enemy systems have been extensively studied. However, little attention has been paid to pest changing rate and pest resistance in these studies. Therefore, this paper proposes a complex and more realistic Filippov pest-natural enemy system with curved discontinuity boundary by considering Beddington–DeAngelis functional response and pest resistance, as well as incorporating pest changing rate in the threshold control index. Based on the relevant theory of the Filippov system, we analyze a sextic equation and obtain that the proposed Filippov system can have at most six sliding segments. By using qualitative techniques, we discuss the sliding segment and pseudo-equilibrium bifurcations. Numerically, we investigate the local and global sliding bifurcations. It can be detected that one new local sliding bifurcation occurs, which could be called the pseudo-Hopf bifurcation but differs from the traditional pseudo-Hopf bifurcation as it involves two sliding segments with opposite stabilities and generates a sliding limit cycle. We also discover two interesting global sliding bifurcations with novel bifurcation processes, which may be termed triple limit cycle bifurcations as they both relate to the appearance of three nested limit cycles.