Search

Abstract: Taking into account periodic impulsive biological and chemical control for pest management at different fixed moment, a three species prey–predator system with Holling type II functional response was investigated. By using Floquet’s theory and the small amplitude perturbation method, it was obtained that there exists an asymptotically stable preys-eradication periodic solution when the impulsive period is less than some critical minimum value (or the release amount of the predator is larger than some critical maximum value), and the system is permanent under the conditions that both the insecticidal effect and impulsive period are grater than some critical maximum values. Furthermore, it is obtained that IPM is more effective than any single one after comparison. Finally, numerical simulations are carried on to show the complex dynamic behavior of system. [Copyright &y& Elsevier]

Abstract: Considering the impact of harvesting on the coexistence and competitive exclusion of competitive predators, a two-zooplankton one-phytoplankton model with harvesting is proposed and investigated. First, stability criteria of the model is analyzed both from local and global point of view. Second, two types of zooplankton will competitively exclude each other in the absence of harvesting with the zooplankton with the larger threshold persisting. If harvest rates are discriminate, then a dominant zooplankton may occur depending on the harvesting level. Thus, for some harvesting levels, the zooplankton one may persist while for other harvesting levels zooplankton two may persist. Furthermore, the value of the harvesting level and coexistence line are obtained when coexistence occur. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings. [Copyright &y& Elsevier]

Abstract: Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation are established. Our results indicate that over exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population which is in line with reality. Furthermore, the existence of bionomic equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, two integrated pest management models are investigated, which rely on release of infective pest individuals and of natural enemies in a constant amount, together with spraying of pesticides. It is proved that the susceptible pests can be eradicated if the release amount of infected pests is above some threshold or the pesticide effect is above another threshold. Furthermore, permanent conditions are established when an impulsive control is used. Finally, numerical results show that (1) fewer infected pests or pesticides are needed as the impulsive strategy is taken, displaying its positive effect on the pest control; (2) our assumption that the natural enemies of the pests do not catch the infective pests would reduce the level of the susceptible pests. [Copyright &y& Elsevier]

Abstract: An impulsive delayed SI model with variable coefficients and a nonlinear incidence is formulated and analyzed. By introducing three thresholds, we obtain sufficient conditions for eradication and permanence of the disease, respectively. It is shown that the conditions depend on time delay for both the global attractivity of the positive infection-free periodic solution and permanence of the model. Furthermore, our results indicate that the disease will disappear if the ratio of the maximum to minimum of the pulse vaccination rate is lager than some value. The main feature of this paper is that we introduce multi-delays and variable coefficients into the SI model, and exhibit a new method which is applied to investigate this model. Numerical results show that the system we considered has complex dynamics including periodic and quasi-periodic oscillations. [Copyright &y& Elsevier]

The aim of this paper is to construct a numerical method preserving positivity for stochastic age-dependent population equations. We use the balanced implicit numerical techniques to maintain the nonnegative path of the exact solution. It is proved that the Balanced Implicit Method (BIM) preserves positivity and converges with strong order 1/2 under given conditions. Finally, two examples are simulated to verify the positivity and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]