共查询到19条相似文献,搜索用时 171 毫秒
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研究了一类带Ivlev型反应函数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了共存解的先验估计,借助于特征值理论、上下解方法得到了共存解存在的必要条件,采用局部分歧理论构造了共存解的局部分支,并运用全局分歧理论证明了共存解的局部分支可延拓为全局分支.结果表明该全局分支连接了模型的两半平凡解分支.从生物学角度看,当两竞争物种的最大生长率满足一定条件时,两物种可以共存. 相似文献
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一类带Beddington-DeAngelis反应项的捕食模型平衡态的分歧解 总被引:1,自引:0,他引:1
本文利用极值原理,L-S度理论,特征值扰动理论及分歧理论,主要研究了一类带Beddington-DeAngelis反应项的捕食模型在Dirichlet边界条件下的平衡态局部分歧解与全局分歧解,给出了局部分歧解存在的充分条件和稳定性,并且得到其平衡态全局分歧解及其走向。 相似文献
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本文讨论一类具有B-D反应函数和Allee效应的捕食-食饵扩散模型正解的存在性、唯一性和多重性.首先运用不动点指数理论得到了正解存在的充分条件.接着利用特征值的变分原理给出了正解的唯一性条件.最后通过分析极限系统的正解,运用不动点指数理论、分歧理论和扰动理论确定了正解的确切重数和稳定性.讨论结果表明:只要Allee效应... 相似文献
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本文考虑一类带饱和项的自催化反应系统.我们首先讨论了常微分系统Hopf分歧的存在性,得到了渐近稳定的周期解.其次讨论了具有扩散项的偏微分系统,在扩散系数满足一定的条下,得到了次临界的Hopf分歧的存在性,并且利用中心流形约化方法,判断出由该Hopf分歧产生的空间齐次的周期解是渐近稳定的.最后,借助Matlab软件形象地验证和刻画了文中的结论. 相似文献
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本文利用局部分歧理论和局部稳定性理论,讨论了一类具有避难所的两物种间的捕食-食饵模型在非齐次Dirichlet边界条件下分歧解的性质,其功能反应函数为Holling Ⅱ型.利用局部分歧和局部稳定性理论给出了分歧解局部稳定的条件;同时利用度理论得到了局部分歧可以延拓到整体分歧的结论. 相似文献
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竞争-竞争-互惠交错扩散模型是一类强耦合的抛物型方程组,关于该模型时变解的整体存在性的研究结果很少,特别是在高维空间中。本文应用能量估计方法,极值原理和抛物型方程的正则性理论证明了:对竞争种群含弱交错扩散项的竞争-竞争-互惠交错扩散模型,它在任意维空间中存在古典的整体解。 相似文献
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本文讨论了一类带有非线性边界条件的捕食-食饵模型,此模型比相应具有线性边界条件的模型具有更加广泛的应用价值。我们利用格林公式证明了一类特征值问题的所有特征值都是正的,利用局部分歧理论证明了模型正解的存在性,进一步,我们利用扰动理论建立了分歧解的渐近稳定性。为了支持和补充分析结果,我们最后利用Matlab软件进行了数值模拟。 相似文献
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在捕食生态系统中,恐惧因子和食饵避难所都有重要的作用。为此,对一类带恐惧因子和食饵避难所的捕食-食饵反应扩散模型进行了研究。通过分析平衡点特征方程,得到了平衡点的局部渐近稳定性;将不受保护食饵比例作为分支参数,给出了正平衡点 Hopf 分支存在的条件。结果表明:避难所的存在会导致 Hopf 分支,产生空间齐次周期解。扩散的加入会产生新的Hopf分支点,产生空间非齐次周期解。这说明通过设立适当的食饵避难所或者减小捕食者的扩散,有助于物种共存。最后,利用 Matlab 进行数值模拟验证了所得的结论。 相似文献
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In this paper, a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed. The interaction between prey, middle predator and top predator population is investigated. In order to clarify the characteristics of the proposed model, the analysis of existence, uniqueness, non-negativity and boundedness of the solutions of the proposed model are examined. Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained. By using stability analysis of the fractional-order system, it is proved that if the basic reproduction number , the predator free equilibrium point is globally asymptotically stable. The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem. Some numerical examples are given to illustrate the theoretical findings. The impact of harvesting on prey and the middle predator is studied. We conclude that harvesting parameters can control the dynamics of the middle predator. A numerical approximation method is developed for the proposed stochastic fractional-order model. 相似文献
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Costin O Luo G Tanveer S 《Philosophical transactions. Series A, Mathematical, physical, and engineering sciences》2008,366(1876):2775-2788
We describe how the Borel summability of a divergent asymptotic expansion can be expanded and applied to nonlinear partial differential equations (PDEs). While Borel summation does not apply for non-analytic initial data, the present approach generates an integral equation (IE) applicable to much more general data.We apply these concepts to the three-dimensional Navier-Stokes (NS) system and show how the IE approach can give rise to local existence proofs. In this approach, the global existence problem in three-dimensional NS systems, for specific initial condition and viscosity, becomes a problem of asymptotics in the variable p (dual to 1/t or some positive power of 1/t). Furthermore, the errors in numerical computations in the associated IE can be controlled rigorously, which is very important for nonlinear PDEs such as NS when solutions are not known to exist globally.Moreover, computation of the solution of the IE over an interval [0,p0] provides sharper control of its p-->infinity behaviour. Preliminary numerical computations give encouraging results. 相似文献
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Claire M. Postlethwaite Jonathan H. P. Dawes 《Dynamical Systems: An International Journal》2006,21(3):313-336
Robust heteroclinic cycles between equilibria lose stability either through local bifurcations of their equilibria or through global bifurcations. This paper considers a global loss of stability termed a 'resonant' bifurcation. This bifurcation is usually associated with the birth or death of a nearby periodic orbit, and generically occurs in either a supercritical or subcritical manner. For a specific robust heteroclinic cycle between equilibria with complex eigenvalues we examine the codimension-two point that separates the supercritical and subcritical. We investigate the bifurcation structure and show the existence of further bifurcations of periodic orbits. 相似文献
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Rizwan-uddin 《Dynamical Systems: An International Journal》1995,10(1):33-48
The space-independent xenon oscillation problem relevant to power nuclear reactors is studied. Xenon oscillations - both, without temperature feedback and in the presence of temperature feedback - have been analyzed semi-analytically and numerically. The effects of various parameters on the nature of bifurcation are studied. Bifurcation analysis shows that Hopf bifurcation occurs, and it is found that both sub- critical and super-critical Hopf bifurcation can occur in different regions of parameter space. Numerical experiments show that 'outsidey the unstable periodic solutions that exist for the sub-critical Hopf bifurcation case, there exist large amplitude, stable periodic solutions to which the initial conditions, outside the basin of attraction of the stable fixed point, evolve. Though the existence of sub-critical Hopf bifurcation indicates that large amplitude perturbations even in the stable region may lead to initially diverging oscillations, it is reassuring that the oscillation amplitude remains bounded 相似文献
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In order to analyse the stability and bifurcation phenomena occurring during expansion of a small void in a rubbery material, the behaviour of spherical shells submitted to a combined far-field pressure and uniaxial tension has been investigated, considering a general nonlinear isotropic elastic compressible behaviour of the material and without any restrictions on the shell thickness. A radial solution for the deformation gradient with a spherical symmetry has been exhibited, which is valid for any behaviour law and consists of a homogeneous deformation. The three-dimensional problem is then linearized around this trivial solution, and we show the existence of a pressure interval containing the zero value, in which the solution is reduced to the trivial solution, which is therefore infinitesimally stable. The condition for stability obtained is compared with Hadamard's condition; particularly, it is shown that both are identical when the material is supposed to have a St Venant-Kirchhoff behaviour law. When the applied pressure lies outside the stability interval, we determine the bifurcation points of the shell around the trivial solution, first when only a pressure is applied and secondly when there is an additional far-field tension, much smaller than the applied pressure. The form of the stress distribution on the boundary of the cavity suggests a possible bifurcation of the spherical solution towards a family of axisymmetric solutions. Within this hypothesis, we get a relation between the geometrical parameter of the shell (its radius and thickness), the mechanical properties of the material and the critical load. The analyses provide evidence of the non-uniqueness of the bifurcation behaviour, since we exhibit some peculiar bifurcation points associated with an infinity of branches of axisymmetric solutions. 相似文献