一类浮游生物捕食系统的全局分歧

主要研究一类在齐次第一边界条件下浮游植物和浮游动物的捕食-食饵模型。给出了平衡态方程解的先验估计。利用分歧理论,以b为分歧参数,得到平衡态系统正解的存在性,将局部分歧延拓为全局分歧。结果表明连通分支C延伸向无穷。     

一类比率依赖的Holling-Leslie捕食-食饵模型的全局分歧

研究了一类基于比率依赖的Holling-Leslie捕食-食饵扩散模型,运用分歧理论和Leray-Schauder度理论的知识,以捕食者的扩散系数为分歧参数,讨论了发自正常数平衡态的局部分支解的存在性,并将局部分歧延拓为整体分歧,从而得到非常数正平衡态存在的充分条件,给出了一维情况下整体分歧解的性态。     

一类带阶段结构的捕食-食饵扩散系统的稳定性

证明一类带有阶段结构和空间扩散的三次捕食者-食饵扩散系统在齐次Neumann边界条件下正解的整体性态,应用谱分析方法和构造Lyapunov泛函讨论系统非负平衡解的渐近稳定性。     

一类竞争模型分歧解的存在性和稳定性

在Dirichlet边界条件下研究了一类具有扩散的两物种竞争模型平衡态正解的存在性和稳定性。运用分歧理论和标准的椭圆型方程正则性理论分析了平衡态分歧解的存在性,得到了其存在的充分条件,并通过数值模拟验证了该条件。利用线性稳定性理论得到了分歧解稳定的条件。研究结果表明,当参数满足一定条件时,系统达到稳定的共存态。     

一个含有扩散的捕食者—食饵—领地生态模型平衡态的稳定性*

本文对含有扩散的捕食者－食饵－领地生态模型进行了讨论，通过构造该系统的不变区域，给出了正整体解存在和有界的范围，同时对其平衡态的稳定性分析提出了一种新的方法－－分域估计法，由此得到了全局渐近稳定的条件。     

具有阶段结构及B-D功能反应的食饵-捕食模型

研究一类食饵具有阶段结构及Beddington-DeAngelis功能反应的食饵-捕食模型的稳定性,利用特征根法,讨论了捕食者灭绝平衡点及食饵和捕食者共存平衡点的局部稳定性;通过引入新的引理,利用微分方程比较定理及迭代法,得到了捕食者灭绝平衡点和食饵、捕食者共存平衡点全局稳定的充分条件;数值模拟验证了主要结果。     

带有乘法Allee效应的捕食-食饵模型的共存解

讨论了一类带有乘法Allee效应的捕食-食饵扩散模型正解的存在性和稳定性。利用局部分歧理论研究了分歧正解的存在性,考察了分歧解的稳定性,运用全局分歧定理将局部分歧进行延拓从而得到了正解存在的充分条件。结果表明当参数满足一定条件时,两物种能共存而且共存解稳定。     

一类捕食-食饵模型平衡解的整体分歧

利用分歧理论和谱分析的方法研究了一类捕食-食饵模型平衡解的整体分歧,得到了在以[d]为分歧参数的条件下,系统在半平凡解[(θ,0)]附近出现分歧现象,得到了该模型正解存在的充分条件。     

多时滞SI模型的稳定性和Hopf分支

建立并分析了一个带有多时滞的捕食者和食饵都染病的SI模型,用特征根的方法求得了它的非负平衡点。通过分析得到当易感食饵的感染率小于某一阈值时,染病食饵和捕食者将最终灭绝。当易感食饵的感染率大于某一阈值且易感捕食者的转化系数小于某一阈值时,捕食者将最终灭绝。边界平衡点是局部渐近稳定的,随着食饵时滞的增加该平衡点由稳定变为不稳定,系统在该平衡点附近发生Hopf分支。捕食者的时滞对该平衡点的稳定性不产生影响。     

一类Leslie-Gower捕食-食饵模型的定性分析

研究一类具有Holling-II型反应函数的Leslie-Gower捕食-食饵模型。给出了平衡态方程解的先验估计,讨论了正常数解的局部渐近稳定性和全局渐近稳定性,利用分歧理论,得到了局部分歧解的存在性,最后将局部分歧延拓为全局分歧。     

Dynamics in a diffusive predator–prey system with ratio-dependent predator influence

A diffusive predator–prey system with predator functional response subject to Neumann boundary conditions is considered. Existence, nonexistence, and boundedness of positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. Hopf and steady-state bifurcation analyses are carried out in detail. These results provide theoretical evidences to the complex spatio-temporal dynamics found by numerical simulation.     

一类种内相食捕食系统非常数正解的存在性

运用谱分析、拓扑度理论和分歧理论的方法,在齐次Neumann边界条件下,研究了一类具有种内相食现象的捕食模型非常数正解的存在性。讨论了正常数解的稳定性,给出了正解的先验估计,讨论了非常数正解的存在性,以扩散系数d₂为分歧参数,讨论了发自正常数解的分歧。     

Positive periodic solutions of neutral predator–prey model with Beddington–DeAngelis functional response

By using a continuation theorem based on coincidence degree theory, some new sufficient conditions are obtained for the existence of positive periodic solutions for a neutral predator–prey model with the Beddington–DeAngelis functional response.     

Periodic solutions for a delayed predator–prey system with stage-structured predator on time scales

In this paper, a modified delayed predator–prey system with stage structure for predator is proposed and studied, which generalizes and incorporates as special cases some known models. With the help of continuation theorem based on the Gaines and Mawhin coincidence degree theory, we investigate the existence of periodic solutions for the proposed delayed predator–prey system with stage-structured predator and two kinds of functional responses (called Holling III functional response and Beddington–DeAngelis functional response) on time scales. In particular, when the time scale is chosen as the set of the real numbers or the integers, the existence of the periodic solutions of the corresponding continuous-time and discrete-time models follows.     

Stability and bifurcation in a stage-structured predator–prey system with Holling-II functional response and multiple delays

In this paper, we analyse a delayed Holling-II predator–prey system with stage-structure for the prey. At first, we study the stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays at the positive equilibrium by analysing the distribution of the roots of the associated characteristic equation. Then, the explicit formula that determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions from the Hopf bifurcation are established by using the normal form method and centre manifold argument. Finally, some numerical simulations are carried out to support the main theoretical results.     

Positive periodic solutions for the neutral ratio-dependent predator–prey model

By using a continuation theorem based on coincidence degree theory, we obtain some new sufficient conditions for the existence of positive periodic solutions for the neutral ratio-dependent predator–prey model with Holling type II functional response.     

The numerical simulation of periodic solutions for a predator–prey system

In this article, the existence and global stability of periodic solutions for a semi-ratio-dependent predator–prey system with Holling IV functional response and time delays are investigated. Using coincidence degree theory and Lyapunov method, sufficient conditions for the existence and global stability of periodic solutions are obtained. A numerical simulation is given to illustrate the results.     

Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays

In this paper, a Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method. Numerical simulations are carried out to illustrate the main results.     

Prey predator hyperheuristic

Prey predator algorithm is a population based metaheuristic algorithm inspired by the interaction between a predator and its prey. In the algorithm, a solution with a better performance is called best prey and focuses totally on exploitation whereas the solution with least performance is called predator and focuses totally on exploration. The remaining solutions are called ordinary prey and either exploit promising regions by following better performing solutions or explore the solution space by randomly running away from the predator. Recently, it has been shown that by increasing the number of best prey or predator, it is possible to adjust the degree of exploitation and exploration. Even though, this tuning has the advantage of easily controlling these search behaviors, it is not an easy task. As any other metaheuristic algorithm, the performance of prey predator algorithm depends on the proper degree of exploration and exploitation of the decision space. In this paper, the concept of hyperheuristic is employed to balance the degree of exploration and exploitation of the algorithm. So that it learns and decides the best search behavior for the problem at hand in iterations. The ratio of the number of the best prey and the predators are used as low level heuristics. From the simulation results the balancing of the degree of exploration and exploitation by using hyperheuristic mechanism indeed improves the performance of the algorithm. Comparison with other algorithms shows the effectiveness of the proposed approach.     

Stationary patterns of a prey–predator system with a protection zone and cross-diffusion of fractional type

This paper is concerned with the stationary patterns of a prey–predator model with a protection zone and fractional type cross-diffusion for the prey. It is shown that the fractional type cross-diffusion has negative effects on the survival of the prey when the intrinsic growth rate of the predator is positive. Moreover, our mathematical analysis shows that, compared with the results obtained in K. Oeda (2011) and K. Oeda (2012), the large cross-diffusion coefficient and large growth rate of the predator species have some essentially different effects on the profiles of the solutions.