一类具有年龄结构的捕食-食饵反应扩散恒化器模型

为研究物种的死亡率对恒化器模型中物种生存状态的影响,提出一类具有年龄结构的捕食-食饵反应扩散恒化器模型。应用最值原理、一致持续性理论、分歧理论等方法,讨论了模型解的全局存在性,分析了模型半平凡解的稳定性以及解的一致持续性,给出模型稳态解以死亡率为分歧参数的全局分歧结构。结果表明:存在死亡率的临界值,当死亡率小于临界值时物种共存,超过临界值捕食者死亡。     

一类非均匀恒化器竞争模型共存态的全局分歧

研究一类具有质载和代谢物的非均匀恒化器竞争模型的全局分歧.利用最大值原理获得正平衡解的先验估计,借助特征值理论得到正平衡解存在的必要条件.以质载物种的最大增长率a为分歧参数,采用局部分歧理论构造正平衡解的局部分支,利用全局分歧理论证明了正平衡解的局部分支可延拓为全局分支,并分析解的稳定性和全局分歧解的走向.结果表明,该全局分支沿参数a延伸到无穷.从生物学角度看,当质载物种的最大增长率a∈(λ1/(1-q),+∞)时,两物种可以共存.     

一类恒化器模型正平衡解的稳定性

在齐次Neumann条件下研究一类具有能量维持扩散的恒化器模型的稳定性.首先利用最大值原理和Harnack不等式给出平衡态方程正解的先验估计;其次利用谱分析和特征值理论证明正常数平衡解的一致渐近稳定性;最后借助构造Lyapunov函数来证明正常数平衡解的全局渐近稳定性.     

具有质体的非均匀恒化器模型的分歧解及稳定性

讨论一类带有Beddington‐DeAngelis型功能反应函数的非均匀恒化器模型解的存在性及稳定性。首先利用上下解方法与极值原理得到恒化器模型的先验估计,然后利用非线性系统的局部分歧理论得到了恒化器模型正解的局部存在性,并且利用特征值扰动理论得到了局部分歧解的稳定性。     

C—M型反应函数的非均匀恒化器竞争模型的全局分歧

研究N维情况下具有C—M型功能反应函数的非均匀恒化器竞争模型．应用局部分歧理论,讨论该模型方程组平衡态非负非平凡局部分歧解的存在性及稳定性;依据全局分歧理论,分析该系统全局分歧解的存在性及其性态．说明当选取适当参数时,2种微生物可共存．     

动脉粥样硬化模型平衡解的研究

利用特征值原理、稳定性理论和局部分歧理论,研究了一类炎症性病变的动脉粥样硬化模型．讨论了该模型的非赞常数平衡解的稳定性,以d2为分歧参数研究了其发自常数平衡解己,。的局部分歧,得到非常数平衡解的存在性．     

具有避难所的Leslie-Gower捕食系统的时空分歧

研究一类修正的具有食饵避难所的Leslie-Gower捕食-食饵模型。给出该模型非常数解的全局吸引子和持续共存性。得到该模型正平衡解的局部渐近稳定性,并通过构造Lyapunov函数得出正平衡解全局稳定的充分条件。利用分歧理论,以d为分歧参数,讨论了此模型在一维空间区域上的Hopf分歧与稳态分歧。     

一类浮游生物捕食-食饵模型的分歧解

研究了一类海洋生态系统中浮游生物捕食-食饵模型平衡态正解的存在性,其功能反应函数为HollingⅡ型.利用线性稳定性理论得到正常数平衡解的稳定性.借助分歧理论,以扩散系数为分歧参数,构造了发自正常数平衡解分支的非常数平衡解分支,从而给出了模型非常数平衡态正解的存在性.     

一类捕食-食饵模型正平衡解的存在性

研究了一类在齐次Dirichlet边界条件下的Holling-Ⅳ型捕食-食饵模型正平衡解的存在性.首先,将该模型等价为椭圆边值问题,对正解做出先验估计.然后,利用度理论和锥映射的不动点计算方法,再结合算子谱分析,得出该模型存在正平衡解的充分条件.结果表明,该模型正平衡解的存在性与模型的导算子的特征值密切相关.     

Holling-Ⅱ型和Beddington-DeAngelis响应函数捕食模型的定性分析

考虑了一类齐次Neumann边界条件下两物种竞争同一种食饵的捕食模型的反应扩散方程组及其对应的平衡态问题,其功能响应函数分别是Holling-Ⅱ型和Beddington-DeAngelis型.利用比较原理研究了解的大时间性态,其中包括耗散性、持久性、半平凡解的稳定性.借助于最大值原理给出了正确的先验估计,并讨论了随着参数的变化非常数正平衡解的不存在性.在一维情形下利用线性化方法,分歧理论研究了半平凡解处的局部分歧,而且得出局部分歧可以延拓到全局分歧即给出了一定条件下正确的存在性.     

Model to couple anaerobic process kinetics with biological growth equilibrium thermodynamics

Monod kinetics indicates a substrate concentration limit (S(min)) at biological growth equilibrium where growth is just balanced by decay. A relationship between S(min) and the Gibbs free energy available at growth equilibrium (ΔG(E)) was introduced into the Monod model and applied directly to chemostat cultures. Results from four anaerobic mixed-culture chemostat studies yielded ΔG(E) of -17.7 ± 2.2 kJ/mol acetate converted to methane. ΔG(E) for propionate syntrophs in propionate-fed cultures was -8.0 ± 3.1 kJ/mol propionate, compared with that of -3.0 ± 0.9 kJ/mol H(2) for the hydrogenotrophs present. With ethanol present, however, ΔG(E) for the hydrogenotrophs became more favorable, -6.1 ± 1.6 kJ/mol H(2), while ΔG(E) for propionate became positive even though propionate was consumed, suggesting an alternative interspecies electron transport route. The results suggest that S(min), normally considered a function of an organism's intrinsic rate characteristics, is also a function of solution characteristics, and this is likely the case for the substrate affinity coefficient, K, as well. A comparison between ΔG(E) and S(min) and reported threshold thermodynamic and concentration limits, leads to the conclusion that ΔG(E) and S(min) represent lower and upper bounds, respectively, on such values. This study indicates that knowledge gained from pure-culture studies applies well to more complex natural anaerobic systems.     

Competitive growth of Gordonia and Acinetobacter in continuous flow aerobic and anaerobic/aerobic reactors

Gordonia amarae and Acinetobacter calcoaceticus pure culture experiments were conducted in continuous flow chemostats fed with an acetate/mineral salts medium under aerobic and anaerobic-aerobic conditions. The growth parameters such as volatile suspended solids (VSS) suggest that Acinetobacter can successfully out-compete Gordonia under both aerobic and anaerobic-aerobic conditions when both are present in a dual culture. Gordonia was reduced to near detection limits (<10 mg VSS/1), while Acinetobacter successfully grew to about 300 mg VSS/1 when both were grown as a dual culture in a single-stage aerobic chemostat with an initial concentration of 200 mg VSS/1 each. In a two-stage anaerobic-aerobic chemostat with recycling, Gordonia was completely washed out in about 24 h, whereas, Acinetobacter successfully grew to over 170% of its initial concentration. In a single-stage aerobic chemostat, a mathematical model describing the competitive growth of the two species based on single culture kinetic parameters predicted Gordonia washout in <30, and the same was observed from experiments. The model predicted an Acinetobacter concentration of 200% of its initial concentration in about 30 h, while experimentally this value was about 150%. Under anaerobic-aerobic conditions, the two-stage model predicted Gordonia washout and an Acinetobacter concentration of about 170% of the initial concentration. The experimental results agreed with the prediction, but the decrease in the Gordonia and increase in the Acinetobacter concentrations were much more rapid than predicted by the model.     

一类非均匀恒化器食物网的共存态

讨论一类带有Beddington-DeAngelis型功能反应函数的非均匀恒化器食物网模型的共存态;该模型除了营养物以外,还包含2个捕食者种群和一个食饵种群.应用Dancer不动点指数和度理论的知识,给出了该系统共存态的充分和必要条件.     

一类改进的Leslie-Gower模型平衡态解的稳定性分析

研究食饵种群具有Crowley-Martin功能反应项和捕食者种群带有经典的Leslie反应项的一类改进的Leslie-Gower模型.首先给出模型平衡解的先验估计,其次研究模型常数正解的存在与唯一性条件,再利用卡尔丹公式解出常数正解值.最后通过构造Lyapunov函数,讨论其常数正解的全局渐近稳定性.     

一类具有媒体报道的SEIRS传染病模型的动力学分析

研究一类受媒体报道影响的SEIRS传染病模型的动力学行为,寻求决定疾病绝灭与否的基本再生数.利用线性化方法和Liapunov函数方法,讨论该模型无病平衡点的全局渐近稳定性和正平衡点的局部渐近稳定性.利用持久性理论证明了模型的持久性.最后通过数值模拟对理论结果进行验证.     

具有接种与治疗的肺结核模型稳定性分析

建立具有接种和不完全治疗的肺结核模型,讨论其平衡点的存在性和稳定性,定义了模型的基本再生数,得到了疾病绝灭与否的阈值R0,并通过运用LaSalle不变原理和构造Lyapunov函数,证明了无病平衡点和地方病平衡点的全局稳定性,即当R0≤1时,该肺结核模型仅存在无病平衡点E0,且E0全局渐近稳定;当R01时,该模型存在无病平衡点E0和地方病平衡点E*,且E*是全局渐近稳定的.