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1.
研究一类带有分段常数变量和避难所的天敌-害虫模型的稳定性和分支行为.首先通过计算转化得到天敌-害虫模型对应的差分模型,利用线性稳定性理论讨论了正平衡态局部渐近稳定的充分条件.其次以害虫种群的内禀增长率或逃脱率为分支参数,利用分支理论研究了模型正平衡态处产生翻转分支周期解和Neimark-Sacker分支周期解的充分条件;并且使用正规形理论和中心流形定理构造了判断分支周期解稳定性的阈值.最后数值模拟验证了理论分析的正确性,并展示了该模型复杂的动力学行为.  相似文献   

2.
讨论了一类具有限时滞含迁移的Prey-Predator系统平衡态的稳定性和Hopf分支,表明当系统的6个独立参数在一定范围内取值时,随着时滞的增加,系统平衡态的稳定性在一定范围内交替变化,而每一次平衡态稳定性的改变都相伴有Hopf分支发生.  相似文献   

3.
本文讨论一年龄结构乙肝传染病模型,得出基本再生数■的表达式,证明:当■1时,无病平衡态局部渐近稳定且全局渐近稳定;当■ 1时,存在唯一的地方病平衡态,并给出地方病平衡态的局部渐近稳定性条件,这些条件对于控制疾病的传播具有重要的理论及实际意义.  相似文献   

4.
利用比较原理,分歧理论,特征值线性扰动理论,主要研究了一类具有饱和与竞争反应项的捕食-食饵系统在Dirichlet边界条件下的平衡态分歧解.首先给出了一个先验估计和局部分歧解存在的充分条件.然后对局部分歧解进行了全局延拓,得到了该系统平衡态的全局分歧解及其走向.最后讨论了局部分歧解的稳定性.  相似文献   

5.
研究了参数依赖时滞的Nicholson生态模型的稳定性和分支问题.利用几何分析方法和摄动法,给出了系统唯一正平衡态的稳定性和Hopf分支存在条件,得到了分支周期解的近似解析表达式和周期解稳定性判别式,通过若干实例验证了理论分析和数值计算的一致性.  相似文献   

6.
讨论了一类改进的Leslie-Gower和Holling-Type Ⅱ型捕食-食饵模型对应的平衡态系统正解的结构.以捕食者的出生率b为分歧参数,利用局部分歧理论和整体分歧理论,得到了此平衡态系统正解的存在性与参数b的关系,即当b适当大时,该平衡态系统具有共存正解.  相似文献   

7.
媒体报道对传染病的感染率有着重要的影响,为探究这种影响建立了一个受媒体影响且具有分段感染率的传染病模型.首先,计算出模型的所有平衡态,并根据基本再生数的大小分析了各平衡态的局部稳定性.其次,通过排除极限换的存在性证明了平衡态的全局渐近稳定性.最后,对媒体影响传染病模型的动力学性态进行了讨论.  相似文献   

8.
研究了周期区域上平衡态附近Landau-Fermi-Dirac方程的Cauchy问题.利用宏观-微观分解以及局部的守恒律得到一致空间能量估计.接着结合对非线性碰撞算子的细致估计,推导了包含随时间演化的等价瞬时能量的非线性能量估计,进而得到一致的先验估计.最后通过局部存在性、一致的先验估计以及连续性技巧,得到了Landau-Fermi-Dirac方程平衡态附近整体光滑解的存在性.  相似文献   

9.
运用泛函分析中的谱理论和非线性发展方程的齐次动力系统理论,讨论了总人口规模变化情况下的年龄结构的SEIR流行病模型.得到了与总人口增长指数λ*有关的再生数R0的表达式,证明了当R0<1时,系统存在唯一局部渐近稳定的无病平衡态;当 R0>1时,无病平衡态不稳定,此时存在地方病平衡态,并在一定条件下证明了地方病平衡态是局部渐近稳定的.  相似文献   

10.
研究了一类具有时滞和空间扩散的SIR传染病模型,通过分析相应的特征方程,讨论了系统每个平衡态的局部稳定性,通过运用交叉迭代方法和Schauder不动点定理,把行波解的存在性转化为一对上下解的存在性,通过构造一对上下解,得到了连接无病平衡态和地方病平衡态的行波解的存在性.  相似文献   

11.
The FitzHugh-Nagumo (FHN) equations are model equations for nerve cell behavior. They support traveling wave solutions which depend on certain parameters. In this paper, a two parameter study of rotating wave solutions (i.e. periodic wavetrains) are considered. These solutions arise from bifurcations of stationary equilibria. The local bifurcation equations are analyzed to determine bifurcation directions as functions of the parameters. In addition, dependence on parameters is computed by numerical continuation and properties of the rotating wave solutions are summarized in parameter space. Finally, some of the biological implications are discussed.  相似文献   

12.
In this paper, bifurcation and stability of two kinds of constant stationary solutions for non-reversible amplitude equations on a bounded domain with Neumann boundary conditions are investigated by using the perturbation theory and weak nonlinear analysis. The asymptotic behaviors and local properties of two explicit steady state solutions, and pitch-fork bifurcations are also obtained if the bounded domain is regarded as a parameter. In addition, the stability of a new increasing or decaying local steady state solution with oscillations are analyzed.  相似文献   

13.
We study the Falk model system describing martensitic phase transitions in shape memory alloys. Its physically closed stationary state is formulated as a nonlinear eigenvalue problem with a non‐local term. Then, some results on existence, stability, and bifurcation of the solution are proven. In particular, we prove the existence of dynamically stable nontrivial stationary solutions. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

14.
运用谱分析和分歧理论的方法,在齐次Dirichlet边界条件下,对具有饱和项的互惠系统的非负定态解的分歧及其稳定性进行研究.一方面,分别以生长率作为分歧参数,讨论了发自半平凡解的分歧;另一方面,以两物种的生长率作为分歧参数,利用Liapunov-Schmidt过程,研究了在二重特征值处的分歧;同时判定了这些分歧解的稳定性.  相似文献   

15.
Two dynamical systems describing the circadian fluctuation of two proteins (PER and TIM) in cells are compared. A simplified model with two variables has already been investigated. Detailed study of the possible bifurcation has been carried out. Periodic solutions of the differential equations with 24-h period have been obtained numerically. Here the general, more realistic model having three variables is investigated. The possible phase portraits and local bifurcations are studied in detail. The saddle-node and Hopf-bifurcation curves are determined in the plane of two parameters by using the parametric representation method. Using these curves the number and the type of the stationary points can be determined. The relation of the two bifurcation curves and the Takens–Bogdanov bifurcation points are also studied. The bifurcation curves are compared to those obtained for the simplified two-variable system.  相似文献   

16.
The semiclassical equations describing a ring laser show two successive bifurcations, one stationary and one Hopf bifurcation. This phenomenon is analyzed mathematically. The initial value problem for the laser equations and the stability of the stationary solutions are discussed in detail. The transition to ultrashort laser pulses is shown to be a Hopf bifurcation. The direction of the bifurcation is determined for a numerical example. It turns out that it depends on the parameters of the system.  相似文献   

17.
一类互惠共存系统的定态分歧与稳定性   总被引:6,自引:0,他引:6  
一类互惠共存系统的定态分歧与稳定性李大华,傅一平(华中理工大学数学系,武汉430074)基金项目:国家自然科学基金资助项目.1)现在江西省九江师范专科学校工作,邮政编码332000.1992年5月6日收到.一、引言在文[1]中R.M.May提出了一个...  相似文献   

18.
This paper is concerned with the bifurcation structure of positive stationary solutions for a generalized Lotka–Volterra competition model with diffusion. To establish the structure, the bifurcation theory and the interval arithmetic are employed.  相似文献   

19.
This paper is devoted to study the bifurcation phenomenon for scalar conservation laws with flux functions involving discontinuous coefficients. In order to deal with it, the special Cauchy initial data are taken and the interactions of stationary wave discontinuities with shock waves and rarefaction waves are considered in detail. The global solutions of this special Cauchy problem are constructed completely when the bifurcation phenomena appear in their solutions.  相似文献   

20.
This paper is concerned with the bifurcation analysis for a free boundary problem modeling the growth of solid tumor with inhibitors.In this problem,surface tension coefficient plays the role of bifurcation parameter,it is proved that there exists a sequence of the nonradially stationary solutions bifurcate from the radially symmetric stationary solutions.Our results indicate that the tumor grown in vivo may have various shapes.In particular,a tumor with an inhibitor is associated with the growth of protrusions.  相似文献   

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