A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of pr...A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory.展开更多
Considering the influence of sublethal concentration of pesticides on pests and natural enemies,we propose a pest-management model with impulsive effect on chemical control and biological control strategies periodic s...Considering the influence of sublethal concentration of pesticides on pests and natural enemies,we propose a pest-management model with impulsive effect on chemical control and biological control strategies periodic spraying pesticide and releasing predatory natural enemies.By using the Floquet theory and the comparison theorem of impulsive differential equations,a sufficient condition for the global asymptotic stability of the pest-eradication periodic solution is obtained.The persistence of the system is further studied,and a sufficient condition for the persistence of the system is obtained.Finally,some numerical simulations are shown to verify our theoretical works.Our works indicate that the sublethal effects of insecticides and the release of predatory natural enemies play significant roles in pest control in agricultural production.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（10771179） Supported by the Natural Science Foundation of the Education Department Henan Province（2007110028）
文摘A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory.
基金supported by the National Natural Science Foundation of China(No.12261018)Youth Science and Technology Talent Growth Project of Guizhou Provincial Department of Education(KY[2018]341,KY[2018]157).
文摘Considering the influence of sublethal concentration of pesticides on pests and natural enemies,we propose a pest-management model with impulsive effect on chemical control and biological control strategies periodic spraying pesticide and releasing predatory natural enemies.By using the Floquet theory and the comparison theorem of impulsive differential equations,a sufficient condition for the global asymptotic stability of the pest-eradication periodic solution is obtained.The persistence of the system is further studied,and a sufficient condition for the persistence of the system is obtained.Finally,some numerical simulations are shown to verify our theoretical works.Our works indicate that the sublethal effects of insecticides and the release of predatory natural enemies play significant roles in pest control in agricultural production.
