共查询到20条相似文献，搜索用时 15 毫秒
1.
The investigation of predator cooperative hunting and prey refuge is crucial for understanding ecological dynamics. In recent years, the role of cooperative hunting or prey refuge in predator-prey systems has received much attention from researchers. However, the study on the combined effects of predator cooperation and predator-dependent prey refuge in the predation system has not yet been investigated. Therefore, in this paper, we propose a prey-predator model with both the factors of predator-dependent prey refuge and cooperative hunting. The positivity and boundedness of the system''s solutions are investigated, followed by the existence and local stability of the equilibrium points. Sufficient conditions for the existence of Hopf bifurcation of the system are obtained. The direction of Hopf bifurcation in the system is investigated by using the center manifold theorem and normal form method. From the analysis of the model, we find that the dependence coefficient $m$ of the prey refuge ratio on the number of predators may be responsible for the stability of the system. The results also indicate that suitable competition coefficients $s$ and cooperative hunting coefficients $alpha$ between predators may enable the species to coexist in the long run. Furthermore, we observe two limit cycles of the system when the parameters satisfy certain conditions. Finally, the dynamical behavior of the model is performed through intriguing numerical simulations. 相似文献
2.
In this paper, we studied a diffusive predator-prey model with a functional response increasing in both predator and prey densities. The Turing instability and local stability are studied by analyzing the eigenvalue spectrum. Delay induced Hopf bifurcation is investigated by using time delay as bifurcation parameter. Some conditions for determining the property of Hopf bifurcation are obtained by utilizing the normal form method and center manifold reduction for partial functional differential equation. 相似文献
3.
In this paper, we propose a diffusive predator-prey model with hunting cooperation and nonlocal competition. Under a rather general selection of the kernel function, we first study the stability of the positive equilibrium of the model. Then, we obtain the conditions which Hopf bifurcation and Turing bifurcation occur. Our results show that nonlocal competition plays an important role in determining the dynamics of the model. 相似文献
4.
This article is concerned with the local stability of a positive equilibrium and the Hopf bifurcation of a delayed three-species food-chain system with the Holling type-II functional response. Some new sufficient conditions ensuring the local stability of a positive equilibrium and the existence of Hopf bifurcation for the system are established. Some explicit formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions using the normal form theory and the centre manifold theory. Numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are included. 相似文献
5.
Yingguo Li 《Annals of Differential Equations》2014,(3):312-317
In this paper,a predator-prey ecosystem with two delays is considered.Firstly,the stability of the equilibrium of the system is investigated by analyzing the characteristic equation.Secondly,by choosing the sum of the two delays as a bifurcation parameter,it is shown that Hopf bifurcation occurs as the parameter passes through a certain critical value.Finally,in order to illustrate our theoretical analysis,some numerical simulations are also included. 相似文献
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7.
该文考虑一类食饵染病的时滞捕食被捕食模型. 作者分析了系统的非负不变性, 边界平衡点的性质和全局稳定性. 证明了当时滞τ=τ-1+τ-2适当小时, 正平衡点是局部渐近稳定的,随着时滞的增加, 正平衡点由稳定变为不稳定, 系统在正平衡点附近发生Hopf分支. 相似文献
8.
本文考虑了存在生产滞后的 Furuno两部门经济增长模型 .给出了此模型资本 -劳动比 k的稳定性和振荡性 ,分析了生产周期时滞对 k稳定性区域的影响 .进一步利用 Hopf分支的方法讨论了 Furuno模型存在周期轨道的条件 . 相似文献
9.
In this paper, the dynamics of a diffusive delayed predator-prey model with herd behavior and prey harvesting subject to the homogeneous Neumann boundary condition is considered. Firstly, choosing the harvesting term as a bifurcation parameter, then we obtain the existence and the stability of the equilibrium by analyzing the distribution of the roots of associated characteristic equation. Secondly, time delay is regarding as a bifurcation parameter, and the use of the normal form theory and center manifold theorem, the existence, stability and direction of bifurcating periodic solutions are all demonstrated detailly. Finally, summarizing some numerical simulations to illustrate the theoretical analysis. 相似文献
10.
ABSTRACT. . This paper aims to study the effect of time‐delay and combined harvesting on a Michaelis‐Menten type ratio‐dependent predator‐prey system. Dynamical behaviors such as persistence, stability, bifurcation, et cetera, are studied critically. Computer simulations are carried out to illustrate our analytical findings. 相似文献
11.
Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response 总被引：1，自引：0，他引：1
Zhihua Liu 《Journal of Mathematical Analysis and Applications》2004,296(2):521-537
We consider a delayed predator-prey system with Beddington-DeAngelis functional response. The stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhães. An example is given and numerical simulations are performed to illustrate the obtained results. 相似文献
12.
Recent manipulations on vertebrates showed that the fear of preda-
tors, caused by prey after they perceived predation risk, could reduce the prey''s
reproduction greatly. And it''s known that predator-prey systems with fear ef-
fect exhibit very rich dynamics. On the other hand, incorporating the time
delay into predator-prey models could also induce instability and oscillations
via Hopf bifurcation. In this paper, we are interested in studying the com-
bined effects of the fear effect and time delay on the dynamics of the classic
Lotka-Volterra predator-prey model. It''s shown that the time delay can cause
the stable equilibrium to become unstable, while the fear effect has a stabi-
lizing effect on the equilibrium. In particular, the model loses stability when
the delay varies and then regains its stability when the fear effect is stronger.
At last, by using the normal form theory and center manifold argument, we
derive explicit formulas which determine the stability and direction of periodic
solutions bifurcating from Hopf bifurcation. Numerical simulations are carried
to explain the mathematical conclusions. 相似文献
13.
不同于以往研究网站竞争系统时,仅考虑带有自反时滞或竞争时滞的情况,本文研究了一类同时带有竞争时滞和自反时滞的网站竞争系统,并以时滞作为分支参数,通过分析正平衡点处的特征方程,研究了正平衡点的稳定性,证明了Hopf分支的存在性,得到了发生Hopf分支时的临界的时滞值,最后通过数值模拟进一步验证了所得结论. 相似文献
14.
本文研究一类含两相异时滞的捕食－被捕食系统的稳定性及分歧。首先，我们讨论两相异时滞对系统唯一正平衡点的稳定性的影响，通过对系数与时滞有关的特征方程的分析，建立了一种稳定性判别性。其次，将一个时滞看成分歧参数，而另一个看作固定参数，我们证明了该系统具有HOPF分歧特性。最后，我们讨论了分歧解的稳定性。 相似文献
15.
Miao Peng Zhengdi Zhang Xuedi Wang Xiuyu Liu 《Journal of Applied Analysis & Computation》2018,8(3):982-997
In this paper, a delayed predator-prey system with Holling type III functional response incorporating a prey refuge and selective harvesting is considered. By analyzing the corresponding characteristic equations, the conditions for the local stability and existence of Hopf bifurcation for the system are obtained, respectively. By utilizing normal form method and center manifold theorem, the explicit formulas which determine the direction of Hopf bifurcation and the stability of bifurcating period solutions are derived. Finally, numerical simulations supporting the theoretical analysis are given. 相似文献
16.
首先建立了一类具有时滞的金融模型,该模型以累计利润额为关键因素,接着以τ为参考元素研究了该模型的稳定性及Hopf分叉.发现当τ变化时,该系统的稳定性会发生变化,该模型会在某一确定值处出现Hopf分叉.最后用中心流形定理和规范型方法研究分叉周期解的稳定性. 相似文献
17.
Yongli Song Tao Yin Hongying Shu 《Mathematical Methods in the Applied Sciences》2017,40(18):6451-6467
In this paper, we investigate the dynamics of a time‐delay ratio‐dependent predator‐prey model with stage structure for the predator. This predator‐prey system conforms to the realistically biological environment. The existence and stability of the positive equilibrium are thoroughly analyzed, and the sufficient and necessary conditions for the stability and instability of the positive equilibrium are obtained for the case without delay. Then, the influence of delay on the dynamics of the system is investigated using the geometric criterion developed by Beretta and Kuang. 26 We show that the positive steady state can be destabilized through a Hopf bifurcation and there exist stability switches under some conditions. The formulas determining the direction and the stability of Hopf bifurcations are explicitly derived by using the center manifold reduction and normal form theory. Finally, some numerical simulations are performed to illustrate and expand our theoretical results. 相似文献
18.
ＴＨＥＭＡＴＨＥＭＡＴＩＣＡＬＢＥＨＡＶＩＯＲＯＦＡＶＯＬＴＥＲＲＡＰＲＥＤＡＴＯＲ─ＰＲＥＹＭＯＤＥＬＷＩＴＨＵＮＤＥＲＣＲＯＷＤＩＮＧＥＦＦＥＣＴＣｈｅｎＬａｎｓｕｎ（陈兰荪）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｃａｄｅｍｉｃＳｉｎ... 相似文献
19.
考虑了一类三维时滞Gause型食物链模型.首先分析了共存平衡点稳定的条件,然后利用多项式理论分析了特征方程特征根的分布,得到了Hopf分支存在的条件,最后给出了几组数值模拟验证文中得到的结论,进一步预测了Hopf分支的全局存在性. 相似文献
20.
根据Klecki思想,对投资过程中具有常数时滞的一类动态宏观经济模型进行了讨论.通过选择时滞作为Hopf分歧参数,当时滞经过临界值时周期行为产生.并用数值例子解释了理论结果. 相似文献