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Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems 被引量:1
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作者 Ayse Feza Güvenilir Billur Kaymakcalan Neslihan Nesliye Pelen 《Applied Mathematics》 2015年第9期1649-1664,共16页
In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessar... In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects. 展开更多
关键词 Time Scales Calculus Predator-Prey Dynamic Systems Periodic Solutions Coincidence Degree Theory beddington-deangelis Type functional response
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Dynamics of a Discrete Predator-Prey System with Beddington-DeAngelis Function Response 被引量:1
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作者 Qibin Fang Xiaoping Li Meiyu Cao 《Applied Mathematics》 2012年第4期389-394,共6页
This paper discusses the dynamic behaviors of a discrete predator-prey system with Beddington-DeAngelis function response. We first show that under some suitable assumption, the system is permanent. Furthermore, by co... This paper discusses the dynamic behaviors of a discrete predator-prey system with Beddington-DeAngelis function response. We first show that under some suitable assumption, the system is permanent. Furthermore, by constructing a suitable Lyapunov function, a sufficient condition which guarantee the global attractivity of positive solutions of the system is 展开更多
关键词 DISCRETE beddington-deangelis functional response PERMANENCE Global ATTRACTIVITY
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EXISTENCE OF PERIODIC SOLUTIONS TO A SYSTEM WITH FUNCTIONAL RESPONSE ON TIME SCALES
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作者 Zhenjie Liu 《Analysis in Theory and Applications》 2009年第4期369-380,共12页
This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By u... This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference equations. 展开更多
关键词 time scale food-chain system beddington-deangelis functional response diffusion coincidence degree
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POSITIVE EQUILIBRIUM AND ITS STABILITY OF THE BEDDINGTON-DEANGELIS'TYPE PREDATOR-PREY DYNAMICAL SYSTEM 被引量:7
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作者 Xiao Haibin Department of Mathematics, Ningbo University, Zhejiang 315211,China Department of Mathematics, Nanjing University, Jiangsu 210093,China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第4期429-436,共8页
A class of Beddington-DeAngelis' type predator-prey dynamic system with prey and predator both having linear density restriction is considered. By using the qualitative methods of ODE, the existence and uniqueness of... A class of Beddington-DeAngelis' type predator-prey dynamic system with prey and predator both having linear density restriction is considered. By using the qualitative methods of ODE, the existence and uniqueness of positive equilibrium and its global asymptotic stability are analyzed. The direct criterions for local stability of positive equilibrium and existence of limit cycle are also established when inference parameter of predator is small. 展开更多
关键词 density restriction beddington-deangelis type functional response global stability limit cycle.
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一类具有Beddington-DeAngelis功能性反应随机模型的数值模拟
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作者 李瑜 黄东卫 郭永峰 《天津工业大学学报》 CAS 北大核心 2014年第2期76-80,共5页
考虑被捕食者的生长率和捕食者的死亡率分别受到高斯白噪声和泊松白噪声扰动的情况,建立了具有BDA功能性反应的三种群密度的随机演化模型,并利用Milstein方法对系统进行了离散化处理;通过计算机代数Matlab编程,完成了确定系统及随机系... 考虑被捕食者的生长率和捕食者的死亡率分别受到高斯白噪声和泊松白噪声扰动的情况,建立了具有BDA功能性反应的三种群密度的随机演化模型,并利用Milstein方法对系统进行了离散化处理;通过计算机代数Matlab编程,完成了确定系统及随机系统的数值模拟.结果表明:在随机扰动强度很小的情况下,系统会产生有界的混沌状态. 展开更多
关键词 高斯白噪声 泊松白噪声 beddington-deangelis(bda)功能性反应 MILSTEIN方法
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Dynamical behaviors of a diffusive predator-prey system with Beddington-DeAngelis functional response 被引量:1
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作者 Han Er-Dong Guo Peng 《International Journal of Biomathematics》 2014年第3期163-182,共20页
In this paper, we present a diffusive predator prey system with Beddington-DeAngelis funetionM response, where the prey species can disperse between the two patches, and there is competition between the two predators.... In this paper, we present a diffusive predator prey system with Beddington-DeAngelis funetionM response, where the prey species can disperse between the two patches, and there is competition between the two predators. Sufficient conditions for the permanence and extinction of system are established based on the upper and lower solution meth- ods and comparison theory of differential equation. Furthermore, the global asymptotic stability of positive solutions is obtained by constructing a suitable Lyapunov function. By using the continuation theorem in coincidence degree theory, we show the periodicity of positive solutions. Finally, we illustrate global asymptotic stability of the model by a simulation figure. 展开更多
关键词 beddington-deangelis functional response DIFFUSION PERMANENCE extinc-tion periodic solution asymptotic stability.
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Dynamical behaviors of a diffusive predator-prey model with Beddington-DeAngelis functional response and disease in the prey 被引量:1
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作者 WenshengYang 《International Journal of Biomathematics》 2017年第8期283-313,共31页
The dynamical behaviors of a diffusive predator-prey model with Beddington-DeAngelis functional response and disease in the prey is considered in this work. By applying the comparison principle, linearized method, Lya... The dynamical behaviors of a diffusive predator-prey model with Beddington-DeAngelis functional response and disease in the prey is considered in this work. By applying the comparison principle, linearized method, Lyapunov function and iterative method, we are able to achieve sufficient conditions of the permanence, the local stability and global stability of the boundary equilibria and the positive equilibrium, respectively. Our result complements and supplements some known ones. 展开更多
关键词 Predator-prey model beddington-deangelis functional response perma-nence iterative method global stability.
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EXTINCTION OF A DISCRETE COMPETITIVE SYSTEM WITH BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE AND THE EFFECT OF TOXIC SUBSTANCES
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作者 Jiangbin Chen Shengbin Yu 《Annals of Applied Mathematics》 2020年第4期356-378,共23页
In this paper, we consider a discrete competitive system with BeddingtonDe Angelis functional response and the effect of toxic substances. By constructing some suitable Lyapunov type extinction functions, sufficient c... In this paper, we consider a discrete competitive system with BeddingtonDe Angelis functional response and the effect of toxic substances. By constructing some suitable Lyapunov type extinction functions, sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. Our results not only supplement and improve but also generalize some existing ones. Numerical simulations show the feasibility of our results. 展开更多
关键词 discrete competitive system beddington-deangelis functional response EXTINCTION toxic substances
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Hopf bifurcation analysis in a turbidostat model with Beddington.DeAngelis functional response and discrete delay
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作者 Yong Yao Zuxiong Li +2 位作者 Huili Xiang Hailing Wang Zhijun Liu 《International Journal of Biomathematics》 2017年第5期1-25,共25页
In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and... In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and discrete delay are studied. The Hopf bifurcations can be shown when the delay crosses the critical value. Furthermore, based on the normal form and the center manifold theorem, the type, stability and other properties of the bifurcating periodic solutions are determined. Finally, some numerical simulations are given to illustrate the results. 展开更多
关键词 Discrete delay TURBIDOSTAT Hopf bifurcation STABILITY beddington-deangelis functional response.
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Dynamics of a non-autonomous density-dependent predator-prey model with Beddington-DeAngelis type 被引量:1
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作者 Haiyin Li Zhikun She 《International Journal of Biomathematics》 2016年第4期15-39,共25页
The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the ... The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator-prey system conforms to the realistically biological environment. We firstly introduce a sufficient condition for the permanence of the system and then use a specific set to obtain a weaker sufficient condition. Afterward, we provide corresponding conditions for the extinction of the system and the existence of boundary periodical solutions, respectively. ~rther, we get a sufficient condition for global attractiveness of the boundary periodic solution by constructing a Lyapunov function, arriving at the uniqueness of boundary periodic solutions since the uniqueness of boundary periodic solutions can be ensured by global attractiveness. Finally, based on the existence of positive periodic solutions, which can be ensured by the Brouwer fixed- point theorem, we provide a sufficient condition for the uniqueness of positive periodic solutions. 展开更多
关键词 PERMANENCE beddington-deangelis functional response global attractive-ness uniqueness of periodic solutions.
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PERMANENCE OF A NON-AUTONOMOUS BEDDINGTON-DEANGELIS PREDATOR-PREY MODEL WITH TIME DELAY AND IMPULSIVE CONTROLS
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作者 Wenjuan Wang, Jingqi Xin (Dept. of Applied Math., Yuncheng University, Yuncheng 044000, Shanxi) 《Annals of Differential Equations》 2011年第2期214-221,共8页
A non-autonomous predator-prey delay system with Beddington-DeAngelis functional response and impulsive controls is established. A set of sufficient conditions which guarantee the prey and the predator to be permanent... A non-autonomous predator-prey delay system with Beddington-DeAngelis functional response and impulsive controls is established. A set of sufficient conditions which guarantee the prey and the predator to be permanent are obtained. 展开更多
关键词 time delay beddington-deangelis functional response PERMANENCE PREDATOR-PREY impulsive controls
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PERMANENCE OF PERIODIC BEDDINGTONDEANGELIS PREDATOR-PREY SYSTEM IN A TWO-PATCH ENVIRONMENT WITH DELAY
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作者 Jie Xu Naiwei Liu 《Annals of Applied Mathematics》 2017年第2期194-202,共9页
In this paper, we study a two-species periodic Beddington-De Angelis predator-prey model with delay in a two-patch environment, in which the prey species can disperse between two patches, but the predator species cann... In this paper, we study a two-species periodic Beddington-De Angelis predator-prey model with delay in a two-patch environment, in which the prey species can disperse between two patches, but the predator species cannot disperse. On the basis of the comparison theorem of differential equations, we establish sufficient conditions for the permanence and extinction of the system. 展开更多
关键词 predator-prey system beddington-deangelis functional response PERMANENCE time delay
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