Dynamic complexity of a predator-prey model for ipm with nonlinear impulsive control incorporating a regulatory factor for predator releases

Abstract

The suess of integrated pest management depends on spraying the orret amount of pestiides at an appropriate time and releases of natural enemies or pathogens of the pest in appropriate proportions at ritial times, with little ost and minimal effets on the environment. Therefore, ontrol deisions require information on instantaneous killing rates of pestiides and numbers of natural enemies to be released, variables that should depend on the densities of both pest and natural enemy population densities in the field. To desribe suh a ontrol strategy we have proposed a mathematial model of IPM involving releases of natural enemies in relation to a regulatory fator. The threshold ondition for the existene and stability of the pest free periodi solution is provided using a obweb model, the omparison priniple and Floquet theory, whih reveals the effets of nonlinear ontrol ation on pest outbreaks. Bifuration analyses show that the dynamis of the proposed model an be very omplex, inluding multiple attrators and swith-like transition patterns following small random perturbations. Moreover, the random perturbations and nonlinear impulsive ontrol measures ould generate omplex swithing patterns, whih show that the pest population ould have outbreaks in omplex ways due to environmental noise.