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.     

双营养物的非均匀Chemostat模型解的性质

本文讨论双营养物的非均匀Chemostat模型解的性质.通过运用极值原理,上下解方法以及分歧理论得到了正平衡解的存在性,运用稳定性理论证明了正平衡解的稳定性.     

Ergodicity and threshold behaviors of a predator‐prey model in stochastic chemostat driven by regime switching

This paper deals with a stochastic predator‐prey model in chemostat which is driven by Markov regime switching. For the asymptotic behaviors of this stochastic system, we establish the sufficient conditions for the existence of the stationary distribution. Then, we investigate, respectively, the extinction of the prey and predator populations. We explore the new critical numbers between survival and extinction for species of the dual‐threshold chemostat model. Numerical simulations are accomplished to confirm our analytical conclusions.     

Dynamics and steady-state analysis of an unstirred chemostat model with internal storage and toxin mortality

This study proposes and analyzes a reaction–diffusion system describing the competition of two species for a single limiting nutrient that is stored internally in an unstirred chemostat, in which each species also produces a toxin that increases the mortality of its competitors. The possibility of coexistence and bistability for the model system is studied by the theory of uniform persistence and topological degree theory in cones, respectively. More precisely, the sharp a priori estimates for nonnegative solutions of the system are first established, which assure that all of nonnegative solutions belong to a special cone. Then it turns out that coexistence and bistability can be determined by the sign of the principal eigenvalues associated with specific nonlinear eigenvalue problems in the special positive cones. The local stability of two semi-trivial steady states cannot be studied via the technique of linearization since a singularity arises from the linearization around those steady states. Instead, we introduce a 1-homogeneous operator to rigorously investigate their local stability.     

一类新的污染环境下具有时滞增长反应及脉冲输入的Monod恒化器模型的定性分析

考虑了一类新的污染环境下具有时滞增长反应及脉冲输入的Monod恒化器模型．运用离散动力系统的频闪映射,获得了一个‘微生物灭绝’周期解,进一步获得了该周期解全局吸引的充分条件．运用脉冲时滞泛函微分方程新的计算技巧,证明了系统在适当的条件下是持久的,结论还表明该时滞是“有害”时滞．     

Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield

In this paper, we consider a variable yield model of a single-species growth in a well-stirred tank containing fresh medium, assuming the instances of time as triggering factors in which the nutrient refilling process and the removal of microorganisms by the uptake of lethal external antibiotic are initiated. It is also assumed that the periodic nutrient refilling and the periodic antibiotic injection occur with the same periodicity, but not simultaneously. The model is then formulated in terms of autonomous differential equations subject to impulsive perturbations. It is observed that either the population of microorganisms essentially washes out, or more favorably, the system is permanent. To describe this dichotomy, some biologically significant integral conditions are introduced. Further, it is shown that in a certain critical situation, a nontriviai periodic solution emerges via a bifurcation phenomenon. Finally, the dynamics of the model is illustrated with numerical experiments and computer simulations.     

具有时滞的周期非均匀竞争恒化器模型的空间动力学

本文提出了一个具有时滞的周期非均匀单种营养基——双种微生物的竞争恒化器模型,利用半群理论, 获得了该模型解的存在唯一性. 进一步, 建立了该模型的竞争排斥原理, 给出了两竞争物种共存的充分条件.     

具有质载和内抑制剂的非均匀恒化器模型共存解的多重性

本文研究一类具有质载和内抑制剂的非均匀恒化器竞争模型. 基于对第二类极限系统分歧的进一步分析, 我们研究了此模型共存解的多重性和稳定性, 从而在一定条件下得到了模型共存解分歧的确切形状, 验证了已有的数值结果.     

Dynamics of the Stochastic Chemostat Model with Monod-Haldane Response Function

This paper is devoted to the asymptotic dynamics of stochastic chemostat model with Monod-Haldane response function. We first prove the existence of random attractors by means of the conjugacy method and further construct a general condition for internal structure of the random attractor, implying extinction of the species even with small noise. Moreover, we show that the attractors of Wong-Zakai approximations converges to the attractor of the stochastic chemostat model in an appropriate sense.     

Dynamic behaviors of Monod type chemostat model with impulsive perturbation on the nutrient concentration

In this paper, the dynamic behaviors of a Monod type chemostat model with impulsive perturbation are investigated. Using Floquet theory and small amplitude perturbation method, we prove that the microorganism-eradication periodic solution is asymptotically stable if the impulsive period satisfies some conditions. Moreover, the permanence of the system is discussed in detail. Finally, we verify the main results by numerical simulation.