Dynamics of a predator-prey system with sublethal effects of pesticides on pests and natural enemies

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.

Dynamics and Exact Solutions of (1 + 1)-Dimensional Generalized Boussinesq Equation with Time-Space Dispersion Term

We study exact solutions to (1 + 1)-dimensional generalized Boussinesq equation with time-space dispersion term by making use of improved sub-equation method, and analyse the dynamical behavior and exact solutions of the sub-equation after constructing the nonlinear transformation and constraint conditions. Accordingly, we obtain twenty families of exact solutions such as analytical and singular solitons and singular periodic waves. In addition, we discuss the impact of system parameters on wave propagation.

AN SEIRS EPIDEMIC MODEL WITH TWO DELAYS AND PULSE VACCINATION

脉搏种痘是有效、重要的策略根除传染疾病。作者与二延期和脉搏种痘调查一个 SEIRS 流行模型。由使用频闪观测仪的地图决定的分离动态系统，作者获得如果，传染人口灭绝 R Δ【 1，并且传染人口是一致地坚持的如果 R Δ】 1。结果显示脉搏种痘或大脉搏种痘率的一个短时期是一个足够的条件根除疾病。