污染环境下具有时滞增长反应和脉冲输入的单种群模型分析

研究污染环境下具有时滞增长反应和脉冲输入的单种群动力学模型,利用脉冲微分系统讨论营养基和毒素的脉冲输入对单种群物种生长的影响,证明微生物在吸收毒素的情况下灭绝的周期解是全局吸引的,并获得系统持久的条件.研究结果为控制环境中毒素对种群生长的影响提供了理论依据.     

一类污染环境下具有脉冲输入的竞争培养模型的定性分析

本文研究了污染环境下具有脉冲输入的竞争培养模型.利用乘子理论和小振幅扰动法,我们得到了种群灭绝周期解全局渐近稳定的充分条件,同时还得到了种群持久的条件.我们的结果表明环境污染能最终导致种群灭绝.     

脉冲输入毒素对具有阶段结构的单种群生存影响的研究

研究了一类小容量污染环境中脉冲输入毒素对具有阶段结构的单种群生存问题,分别找到了种群生存与灭绝的阈值,利用不等式放缩技巧,得到了种群灭绝和持久生存的充分条件.利用MATLAB数值仿真,验证了理论结果的正确性,分析了毒素输入量,毒素输入周期及种群成长时间对种群生存的影响.     

具有脉冲毒素投放和营养再生的恒化器模型

研究具有脉冲毒素投放和营养再生的恒化器模型.利用脉冲微分方程的比较定理和小扰动方法得到了边界周期解全局渐近稳定的充分条件,进而得到了系统持续生存的充分条件.结果表明毒素环境将会导致微生物种群的灭绝.     

污染喀斯特环境下具瞬时与非瞬时脉冲效应的单种群动力学模型

建立污染喀斯特环境下具瞬时与非瞬时脉冲效应的单种群动力学模型.利用脉冲微分方程理论,得到系统种群持续生存的控制阈值.研究结果表明瞬时脉冲收获量与非瞬时脉冲收获区间长度对于系统种群持久起着重要作用,结论为现实的生物资源管理提供了可靠的策略支持.     

污染环境下毒素脉冲输入和心理效应对随机捕食-食饵系统的影响

文章研究了在污染环境下毒素脉冲输入和心理效应对随机捕食-食饵系统的影响.通过构造Lyapunov函数,证明了系统全局正解的存在性;利用随机微分方程比较定理得到系统平均持续生存与灭绝的充分条件;应用Has'minskii定理证明了系统至少存在一个非平凡的正周期解,并给出了数值模拟.     

污染环境下具有时滞和脉冲输入两种营养基和一种微生物恒化器模型的动力学分析(英文)

本文研究在污染环境下带有时滞和脉冲输入的双营养基和一种微生物的恒化器模型.利用脉冲微分方程比较定理,我们得到微生物灭绝周期解的全局吸引和系统持久的充分条件.     

毒素脉冲输入与种群脉冲出生切换阶段结构单种群动力学模型研究

本文研究了毒素脉冲输入与脉冲出生切换阶段结构单种群动力学模型.利用常微分方程及差分分析,获得了系统种群灭绝和持久生存的控制条件结果,为污染环境中的生物资源管理提供了可靠的管理策略.     

具脉冲出生与脉冲输入环境毒素的单种群动力学模型研究

讨论了在污染的环境中具脉冲出生的单种群动力学模型,证明了系统的所有解是一致有界的.利用数学的分析方法,获得了系统种群灭绝的条件,也得到了系统的持久生存的条件.研究的结果为污染环境中实际生物资源管理提供了可靠的管理策略.     

基于污染环境毒素驱使下扩散的随机单种群系统的生存分析

研究了一类基于污染斑块环境毒素驱使下扩散的单种群模型.通过构造合适的Lyapunov函数分析了系统存在唯一的全局正解,并讨论了解的随机最终有界性;最后获得了种群随机持久、均值持久和灭绝的充分条件.     

Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input

In this paper, we have investigated a predator–prey system in a polluted environment with impulsive toxicant input at fixed moments. We have obtained two thresholds on the impulsive period by assuming the toxicant amount input is fixed to the environment at each pulse moment. If the impulsive period is greater than the big threshold, then both populations are weak average persistent. If the period lies between of the two thresholds, then the prey population will be weak average persistent while the predator population extinct. If the period is less than the small threshold, both populations tend to extinction. Finally, our theoretical results are confirmed by own numerical simulations.     

Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input

Taking both white noises and colored noises into account, a stochastic single-species model with Markov switching and impulsive toxicant input in a polluted environment is proposed and investigated. Sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The threshold between weak persistence and extinction is obtained. Some simulation figures are introduced to illustrate the main results.     

Dynamics of a two-species Lotka-Volterra competition system in a polluted environment with pulse toxicant input

In most models of population dynamics in a polluted environment, the emission of toxicant is generally considered to be continuous, but it is often the case that toxicant is emitted in regular pulses. This paper deals with the effects of pulse toxicant input with constant rate on two-species Lotka-Volterra competition system in a polluted environment. The thresholds between persistence and extinction of each population are obtained. Moreover, our results indicate that the release amount of toxicant and the pulse period will affect the fate of each population. Finally, the results are verified through computer simulations.     

The effects of a single stage-structured population model with impulsive toxin input and time delays in a polluted environment

Uncontrolled contribution of pollutant to the environment has led many species to extinction and several others are at the verge of extinction. This article deals with the dynamics of a single stage-structured population model with impulsive toxin input and time delays (including constant individual maturation time delay and pollution time delay) in a polluted environment, in which we assume that only the mature individuals are affected by pollutants. We obtain conditions for the global attractivity of the population-extinction periodic solution and the permanence of the population. We show that maturation time delay and impulsive toxin input can bring great effects on the dynamics of the system, and pollution time delay is harmless. Numerical simulations confirm our theoretical results.     

EFFECTS OF A TOXICANT ON A SINGLE-SPECIES POPULATION WITH PARTIAL POLLUTION TOLERANCE IN A POLLUTED ENVIRONMENT

We study a model for the long-term behavior of a single-species population with some degree of pollution tolerance in a polluted environment. The model consists of three ordinary differential equations: one for the population density, one for the amount of toxicant inside the living organisms, and one for the amount of toxicant in the environment. We derive sufficient conditions for the persistence and the extinction of the population depending on the exogenous input rate of the toxicant into the environment and the level of pollution tolerance of the organisms. Numerical simulations are carried out to illustrate our main results.     

具有脉冲输入和资源循环的恒化器模型

研究了一类在污染环境下的具有脉冲输入和资源循环的Monod型恒化器模型,利用Floquet定理和脉冲微分方程解的比较定理,我们得出了系统的微生物灭绝周期解全局渐近稳定以及系统持久的充分条件.     

Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment

This paper intends to develop a new method to obtain the threshold of an impulsive stochastic chemostat model with saturated growth rate in a polluted environment. By using the theory of impulsive differential equations and stochastic differential equations, we obtain conditions for the extinction and the permanence of the microorganisms of the deterministic chemostat model and the stochastic chemostat model. We develop a new numerical computation method for impulsive stochastic differential system to simulate and illustrate our theoretical conclusions. The biological results show that a small stochastic disturbance can cause the microorganism to die out, that is, a permanent deterministic system can go to extinction under the white noise stochastic disturbance. The theoretical method can also be used to explore the threshold of some impulsive stochastic differential equations.     

Study of chemostat model with impulsive input and nutrient recycling in a polluted environment

In this paper, we introduce and study a Monod type chemostat model with nutrient recycling and impulsive input in a polluted environment. The sufficient and necessary conditions on the permanence and extinction of the microorganism are obtained. Two examples are given in the last section to verify our mathematical results. The numerical analysis show that if only the system is permanent, then it also is globally attractive.