共查询到19条相似文献,搜索用时 63 毫秒
1.
一类带有扩散的三种群捕食模型的非常数正平衡解 总被引:1,自引:0,他引:1
一类带有扩散和非单调比率依赖响应函数的捕食模型在某些条件下有两个正常数解,讨论了该捕食模型在齐次Neumann边界条件下的非常数正平衡解的存在性和不存在性. 相似文献
2.
本文讨论一个带有交错扩散的捕食模型的齐次Neumann问题.首先,利用Harnack等式以及椭圆方程正则理论讨论了当扩散系数至少一个取极限时非常数正解的渐近性,再利用渐近性质以及奇异扰动方法讨论了当扩散系数取极限的情况下非常数正解的存在性. 相似文献
3.
三种群食物链交错扩散模型的整体 总被引:1,自引:0,他引:1
本文应用能量估计方法和Gagliardo-Nirenberg型不等式证明了一类强耦合反应扩散系统整体解的存在性和一致有界性,该系统是带自扩散和交错扩散项的三种群Lotka-Volterra食物链模型.通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件. 相似文献
4.
本文利用对偶性技巧及一系列非线性分析的方法,研究了一类带有带有扩散影响的拟线性抛物系统解的整体存在性. 相似文献
5.
带有交叉扩散的捕食模型的非常数正稳态解的存在性 总被引:2,自引:0,他引:2
本文研究了下列带有交叉扩散的捕食模型的稳态问题的非常数正解的存在性,证明了当d4>1/m1v-u时存在(g1,d2,d3)使得稳态问题存在非常数正解;而当d4≤1/m1v-u或者d1≥m1v-u/u1或者a(m1b,a2(b))时稳态问题不存在非常数正解. 相似文献
6.
本文考虑了一类带扩散的捕食模型的平衡态问题.首先给出了正解的先验估计,进而,分别借助于能量方法和拓扑度理论得出了因参数的变化而引起的非常数正解的不存在性和存在性结果. 相似文献
7.
讨论了带扩散和交错扩散的三种群捕食模型.应用上下解方法,得到这类捕食模型正解的存在性,同时研究了其正解的不存在性. 相似文献
8.
9.
闫莎 《纯粹数学与应用数学》2011,27(2):225-235
应用能量估计方法和Gagliardo-Nirenberg型不等式证明含一类食饵种群和两类竞争捕食者种群的反应扩散模型整体解的存在性和一致有界性,该模型是带自扩散和交错扩散项的三种群捕食者-食饵模型. 相似文献
10.
本文研究一类具有种内竞争的三种群捕食者-食饵模型的强耦合交错扩散系统,发现当捕食者对食饵的捕获水平高于食饵的种内竞争水平时,捕食者的大的交错扩散系数能够导致Turing不稳定. 相似文献
11.
In this paper, a system of reaction-diffusion equations arising in eco-epidemiological systems is investigated. The equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases. A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given. It is proved that if the diffusion coefficient of the predator is treated as bifurcation parameter, non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions. 相似文献
12.
In this paper we consider a competitor-competitor-mutualist model with cross-diffusion. We prove some existence and non-existence results concerning non-constant positive steady-states (patterns). In particular, we demonstrate that the cross-diffusion can create patterns when the corresponding model without cross-diffusion fails. 相似文献
13.
Qualitative Analysis of a Predator-prey System
with Ratio-dependent and Modified Leslie-Gower
Functional Response
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Jie Song 《Journal of Nonlinear Modeling and Analysis》2020,2(3):317-332
In this paper, a predator-prey model with ratio-dependent and
modified Leslie-Gower functional response subject to homogeneous Neumann
boundary condition is considered. First, properties of the constant positive sta-
tionary solution are shown, including the existence, nonexistence, multiplicity
and stability. In addition, a comparatively characterization of the stability is
obtained. Moreover, the existing result of global stability is improved. Finally,
properties of nonconstant positive stationary solutions are further studied. By
a priori estimate and the theory of Leray-Schauder degree, it is shown that
nonconstant positive stationary solutions may exist when the system has two
constant positive stationary solutions. 相似文献
14.
In this paper, a predator-prey reaction-diffusion system with one resource and two consumers is considered. Assume that one consumer species exhibits Holling II functional response while the other consumer species exhibits Beddington-DeAngelis functional response, and they compete for the common resource. First, it is proved that the unique positive constant steady state is stable for the ODE system and the reaction-diffusion system. Second, a prior estimates of positive steady state is given. Finally, the non-existence of non-constant positive steady state, the existence and bifurcation of non-constant positive steady state are studied. 相似文献
15.
In this paper, spatial patterns of predator-prey model with cross diffusion are investigated. The Hopf and Turing bifurcation critical line in a spatial domain are obtained by using mathematical theory. Moreover, exact Turing space is given in two parameters space. Our results reveal that cross diffusion can induce stationary patterns, which may be useful to help us better understand the dynamics of the real ecosystems. 相似文献
16.
Stationary distribution and persistence of a stochastic predator-prey model with a functional response
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A stochastic predator-prey model with a functional response is investigated in this paper. The asymptotic properties of the stochastic model are considered here. Under some conditions, we show that the stochastic model is persistent in mean. Moreover, the existence of stationary distribution to the model is obtained. Simulations are also carried out to confirm our analytical results. 相似文献
17.
Spatial Dynamics of a Diffusive Predator-prey Model with Leslie-Gower Functional Response and Strong Allee Effect
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In this paper, spatial dynamics of a diffusive predator-prey model
with Leslie-Gower functional response and strong Allee effect is studied. Firstly,
we obtain the critical condition of Hopf bifurcation and Turing bifurcation of
the PDE model. Secondly, taking self-diffusion coefficient of the prey as bi-
furcation parameter, the amplitude equations are derived by using multi-scale
analysis methods. Finally, numerical simulations are carried out to verify
our theoretical results. The simulations show that with the decrease of self-
diffusion coefficient of the prey, the preys present three pattern structures:
spot pattern, mixed pattern, and stripe pattern. We also observe the transi-
tion from spot patterns to stripe patterns of the prey by changing the intrinsic
growth rate of the predator. Our results reveal that both diffusion and the
intrinsic growth rate play important roles in the spatial distribution of species. 相似文献
18.
Uniqueness and stability of steady states for a predator-prey model in heterogeneous environment 总被引:1,自引:0,他引:1
In this paper, we deal with a predator-prey model with diffusion in a heterogeneous environment, and we study the uniqueness and stability of positive steady states as the diffusion coefficient of the predator is small enough.
19.
Xianzhong Zeng 《Journal of Mathematical Analysis and Applications》2007,332(2):989-1009
In this paper, we study a strongly coupled elliptic system arising from a Lotka-Volterra prey-predator system, where cross-diffusions are included in such a way that the prey runs away from the predator and the predator moves away from a large group of preys. We establish the existence and non-existence of its non-constant positive solutions. Our results show that if m1b<a<2m1b/(1−m1m2) when 0<m1m2<1 or a>m1b when m1m2?1, , d2>0, d3?0 and , then there exists (d1,d2,d3,d4) such that the stationary problem admits non-constant positive solutions. Otherwise, the stationary problem has no non-constant positive solution. In particular, the results indicate that its non-constant positive solutions are mainly created by the cross-diffusion d4. 相似文献