共查询到19条相似文献,搜索用时 450 毫秒
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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. 相似文献
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研究了Dirichlet边界条件下具交错扩散的两种群互惠模型.采用上下解方法,结合Schauder不动点理论,给出了问题共存解存在的充分条件.进一步,利用单调迭代序列的方法构造出问题的共存解.结果表明,当交错扩散相对弱时,问题至少存在一共存解. 相似文献
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该文讨论了具有扩散的捕食模型.利用上下解方法和分支理论,得到了椭圆系统的共存解的存在性,并且讨论了共存解的稳定性. 相似文献
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本文研究一类空间异质环境下具有扩散的湖泊生态系统模型.引入空间异质环境影响,模型中浮游动物的扩散及相互作用系数具有空间依赖性.本文首先证明了模型解的全局存在和唯一性以及共存平衡解的存在唯一性,通过构造Lyapunov泛函,建立了模型非齐次共存平衡解的全局渐近稳定性条件,并通过数值模拟验证了理论结果.本文推广了含有外来有机物的湖泊生态系统模型,进一步证明了空间异质环境下的扩散不会改变湖泊生态系统共存平衡解的稳定性. 相似文献
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研究了一类具有外源和内部感染的捕食-食饵模型在Neumann边界条件下的共存态问题.首先利用特征值理论证明了该模型正常数平衡解的渐近稳定性;然后,给出了正平衡解的先验估计;最后利用度理论研究了非常数正平衡解的存在性. 相似文献
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利用重合度理论中的延拓定理,研究了时间尺度上具有变时滞的两个捕食者和一个食饵的共存现象,证明了该捕食与被捕食系统至少一个正周期解. 相似文献
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带B-D反应项的捕食-食饵模型的全局分支及稳定性 总被引:5,自引:0,他引:5
研究了一类带Beddington-DeAngelis反应项的捕食-食饵模型的共存态问题.利用谱分析和分歧理论的方法,分别以a,c为分歧参数,讨论了发自半平凡解的局部分支解的存在性,并将局部分支延拓为整体分支,从而得到正平衡解存在的充分条件;同时判定了局部分支解的稳定性. 相似文献
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This paper deals with the unstirred chemostat model with crowding effects. The introduction of crowding effects makes the conservation law invalid, and the equations cannot be combined to eliminate one of the variables. Consequently, the usual reduction of the system to a competitive system of one order lower is lost. Thus the system with predation and competition is non-monotone, and the single population model cannot be reduced to a scalar system. First, the uniqueness and asymptotic behaviors of the semi-trivial solutions are established. Second, the existence and structure of coexistence solutions are given by the degree theory and bifurcation theory. It turns out that the positive bifurcation branch connects one semi-trivial solution branch with another. Finally, the stability and asymptotic behaviors of coexistence solutions are discussed in some cases. It is shown that crowding effects are sufficiently effective in the occurrence of coexisting, and overcrowding of a species has an inhibiting effect on itself. 相似文献
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This paper is concerned with the dynamics of a two-species reaction–diffusion–advection competition model subject to the no-flux boundary condition in a bounded domain. By the signs of the associated principal eigenvalues, we derive the existence and local stability of the trivial and semi-trivial steady-state solutions. Moreover, the nonexistence and existence of the coexistence steady-state solutions stemming from the two boundary steady states are obtained as well. In particular, we describe the feature of the coincidence of bifurcating coexistence steady-state solution branches. At the same time, the effect of advection on the stability of the bifurcating solution is also investigated, and our results suggest that the advection term may change the stability. Finally, we point out that the methods we applied here are mainly based on spectral analysis, perturbation theory, comparison principle, monotone theory, Lyapunov–Schmidt reduction, and bifurcation theory. 相似文献
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We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response.The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Holling type-II functional response.Here,a positive solution corresponds to a coexistence state of the model.Firstly,we study the sufficient conditions to ensure the existence of positive solutions by using degree theory and analyze the coexistence region in parameter plane.In addition,we present the uniqueness of positive solutions in one dimension case.Secondly,we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system,and then we characterize the stable/unstable regions of semi-trivial solutions in parameter plane. 相似文献
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Hua Nie 《Journal of Mathematical Analysis and Applications》2007,334(2):889-908
This paper deals with a chemostat model with an internal inhibitor. First, the elementary stability and asymptotic behavior of solutions of the system are determined. Second, the effects of the inhibitor are considered. It turns out that the parameter μ, which measures the effect of the inhibitor, plays a very important role in deciding the stability and longtime behavior of solutions of the system. The results show that if μ is sufficiently large, this model has no coexistence solution and one of the semitrivial equilibria is a global attractor when the maximal growth rate a of the species u lies in certain range; but when a belongs to another range, all positive solutions of this model are governed by a limit problem, and two semitrivial equilibria are bistable. The main tools used here include monotone system theory, degree theory, bifurcation theory and perturbation technique. 相似文献
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In this paper, the competitor-competitor-mutualist three-species Lotka-Volterra model is discussed. Firstly, by Schauder fixed point theory, the coexistence state of the strongly coupled system is given. Applying the method of upper and lower solutions and its associated monotone iterations, the true solutions are constructed. Our results show that this system possesses at least one coexistence state if cross-diffusions and cross-reactions are weak. Secondly, the existence and asymptotic behavior of T-periodic solutions for the periodic reaction-diffusion system under homogeneous Dirichlet boundary conditions are investigated. Sufficient conditions which guarantee the existence of T-periodic solution are also obtained. 相似文献
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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. 相似文献
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Feng-Bin Wang 《Journal of Differential Equations》2010,249(11):2866-2888
This paper examines a system of reaction-diffusion equations arising from a flowing water habitat. In this habitat, one or two microorganisms grow while consuming two growth-limiting, complementary (essential) resources. For the single population model, the existence and uniqueness of a positive steady-state solution is proved. Furthermore, the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values. Mathematical analysis for the two competing populations is carried out. More precisely, the long-time behavior is determined by using the monotone dynamical system theory when the semi-trivial solutions are both unstable. It is also shown that coexistence solutions exist by using the fixed point index theory when the semi-trivial solutions are both (asymptotically) stable. 相似文献
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讨论了齐次Neumann边界条件下食饵有外界常收获率的捕食-食饵模型的共存态首先分析了正常数解的稳定性以及非常数正平衡解不存在的条件.其次,基于对平衡解的先验估计,利用拓扑度理论,给出了此平衡态系统非常数正解的存在性. 相似文献