Threshold Strategy for Nonsmooth Filippov Stage‐Structured Pest Growth Models

Abstract

In order to control pests and eventually maintain the number of pests below the economic threshold, in this paper, based on the nonsmooth dynamical system, a two-stage-structured pest control Filippov model is proposed. We take the total number of juvenile and adult pest population as the control index to determine whether or not to implement chemical control strategies. The sliding-mode domain and conditions for the existence of regular and virtual equilibria, pseudoequilibrium, boundary equilibria, and tangent points are given. Further, the sufficient condition of the locally asymptotic stability of pseudoequilibrium is obtained. By numerical simulations, the local bifurcations of the equilibria are discussed. Our results show that the total number of pest populations can be successfully controlled below the economic threshold by taking suitable threshold policy.

Stability and bifurcation analysis of Filippov food chain system with food chain control strategy

“…The modeling and control of the ecological systems and the evolution of species are known to undergo a variety of bifurcation phenomena ranging from multiplicity and stability of steady states to sustained oscillations. Recently, Filippov systems have gained considerable attention in life science and engineering [3,10,11,12,16,20,21,24,31,32,34] and they provide a natural and convenient unified framework for mathematical modeling of several real-world problems. In this paper, we proposed a Filippov food chain model with food chain control strategy to describe three species food chain interaction model composed of x(t), y(t), and z(t).…”