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一类食饵具有阶段结构的时滞Predator-Prey系统的周期解(英文) 被引量:1
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作者 张少林 韦明俊 《浙江科技学院学报》 CAS 2006年第1期1-7,共7页
研究了一类时滞Predator-Prey系统,其中Prey种群是具有两个生命阶段的种群,即幼年阶段和成年阶段。Predator种群只能捕食Prey幼年种群。通过应用Gaines和Mawhin重合度理论的连续函数定理,给出了系统正周期解存在的充分条件。
关键词 重合度 predatorprey系统 正周期解 阶段结构
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Flip bifurcation and Neimark-Sacker bifurcation in a discrete predator prey model with harvesting
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作者 Wei Liu Yaolin Jiang 《International Journal of Biomathematics》 SCIE 2020年第1期1-37,共37页
In this paper,a difference-algebraic predator prey model is proposed,and its complex dynamical behaviors are analyzed.The model is a discrete singular system,which is obtained by using Euler scheme to discretize a dif... In this paper,a difference-algebraic predator prey model is proposed,and its complex dynamical behaviors are analyzed.The model is a discrete singular system,which is obtained by using Euler scheme to discretize a differential-algebraic predator-prey model with harvesting that we establish.Firstly,the local stability of the interior equilibrium point of proposed model is investigated on the basis of discrete dynamical system the­ory.Further,by applying the new normal form of difference-algebraic equations,center manifold theory and bifurcation theory,the Flip bifurcation and Neimark-Sacker bifur­cation around the interior equilibrium point are studied,where the step size is treated as the variable bifurcation parameter.Lastly,with the help of Matlab software,some numerical simulations are performed not only to validate our theoretical results,but also to show the abundant dynamical behaviors,such as period-doubling bifurcations,period 2,4,8,and 16 orbits,invariant closed curve,and chaotic sets.In particular,the corresponding maximum Lyapunov exponents are numerically calculated to corroborate the bifurcation and chaotic behaviors. 展开更多
关键词 predator prey HARVESTING Flip bifurcation Neimark Sacker bifurcation chaos.
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Periodic Solutions of Periodic Delay Predator-Prey System with Nonmonotonic Functional Response 被引量:1
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作者 宋永利 韩茂安 《Journal of Shanghai Jiaotong university(Science)》 EI 2003年第1期107-110,共4页
By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions of a delayed predator prey system with nonmonotonic functional respon... By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions of a delayed predator prey system with nonmonotonic functional response in a periodic environment. 展开更多
关键词 predator prey system periodic solution coincidence degree
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一类含扩散与时滞的Prey-Predator模型的周期解
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作者 徐天华 赵晓东 《重庆文理学院学报(自然科学版)》 2009年第2期32-35,共4页
利用上下解方法以及比较原理研究了一类含扩散与时滞的Prey-Predator模型,证明在一定条件下该模型的零平衡态及半平凡周期解的全局稳定性,并获得了这个系统具有一对周期拟解的充分条件.对任意的非负初值函数,这一对周期拟解构成的区间... 利用上下解方法以及比较原理研究了一类含扩散与时滞的Prey-Predator模型,证明在一定条件下该模型的零平衡态及半平凡周期解的全局稳定性,并获得了这个系统具有一对周期拟解的充分条件.对任意的非负初值函数,这一对周期拟解构成的区间是此系统的一个吸引子. 展开更多
关键词 扩散 时滞 上下解 preypredator模型 周期解
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Stability of the Bifurcation Solutions for a Predator-Prey Model
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作者 孟义杰 王一夫 《Journal of Beijing Institute of Technology》 EI CAS 2003年第2期208-211,共4页
The bifurcation solution of the nonnegative steady state of a reaction diffusion system was investigated. The combination of the sturm type eigenvalue and the theorem of bifurcation was used to study the local coex... The bifurcation solution of the nonnegative steady state of a reaction diffusion system was investigated. The combination of the sturm type eigenvalue and the theorem of bifurcation was used to study the local coexistence solutions, and obtain the stability of bifurcation solutions. The system model describes predator prey interaction in an unstirred chemostat. 展开更多
关键词 reaction diffusion system local bifurcation predator prey maximum principle
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A CONDITION OF THE EXISTENCE OF STABLE POSITIVE STEADY-STATE SOLUTIONS FOR A ONE PREDATOR TWO PREY SYSTEM
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作者 周笠 宋开泰 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1993年第2期111-125,共15页
One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one pred... One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods. 展开更多
关键词 One predator Two prey System Bifurcation Perturbation Stability of Positive Steady-state Solution.
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Turing Instability of Diffusive Predator⁃Prey System with Gompertz Growth
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作者 LI Ying PENG Yahong 《Journal of Donghua University(English Edition)》 CAS 2021年第5期459-464,共6页
This paper mainly focus on the research of a predator⁃prey system with Gompertz growth of prey.When the system does not contain diffusion,the stability conditions of positive equilibrium and the occurring condition of... This paper mainly focus on the research of a predator⁃prey system with Gompertz growth of prey.When the system does not contain diffusion,the stability conditions of positive equilibrium and the occurring condition of the Hopf bifurcation are obtained.When the diffusion term of the system appears,the stable conditions of positive equilibrium and the Turing instability condition are also obtained.Turing instability is induced by the diffusion term through theoretical analysis.Thus,the region of parameters in which Turing instability occurs is presented.Then the amplitude equations are derived by the multiple scale method.The results will enrich the pattern dynamics in predator⁃prey systems. 展开更多
关键词 predatorprey system Gompertz growth stability analysis Turing instability amplitude equation
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A Leslie-Gower Holling Type-II Predator-Prey Mathematical Model with Disease in Prey Population Incorporating a Prey Refuge
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作者 P. Mandal N. Das S. Pal 《Journal of Mathematics and System Science》 2016年第10期395-408,共14页
We formulate and analyze a predator-prey model followed by Leslie-Gower model in which the prey population is infected by disease. We assume that the disease can only spread over prey population. As a result prey popu... We formulate and analyze a predator-prey model followed by Leslie-Gower model in which the prey population is infected by disease. We assume that the disease can only spread over prey population. As a result prey population has been classified into two categories, namely susceptible prey, infected prey where as the predator population remains free from infection. To investigate the behaviour of prey population we incorporate prey refuge in this model. Since the prey refuge decreases the predation rate then it has an important effect in our predator-prey interaction model. We have discussed the existence of various equilibrium points and local stability analysis at those equilibrium points. We investigate the Hopf-bifurcation analysis about the interior equilibrium point by taking the rate of infection parameter and the prey refuge parameter as bifurcation parameters. The numerical analysis is carried out to support the analytical results and to discuss some interesting results that our model exhibits. 展开更多
关键词 predator and prey Disease transmission prey refuge Stability Hopf-bifurcation.
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Effect of random movement and cooperative hunting in the prey-predator system:A dynamical approach
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作者 Shivam Teekam Singh Mukesh Kumar 《International Journal of Biomathematics》 SCIE 2024年第3期211-240,共30页
Self-diffusion prerequisite is obtained as the spreading approach of biological populations.Cooperative hunting is a common behavior in predator populations that promotes predation and the coexistence of the prey-pred... Self-diffusion prerequisite is obtained as the spreading approach of biological populations.Cooperative hunting is a common behavior in predator populations that promotes predation and the coexistence of the prey-predator system.On the other side,the Allee effect among prey may cause the system to become unstable.In this paper,a difusive prey predator system with cooperative hunting and the weak Allee effect in prey populations is discussed.The linear stability and Hopf-bifurcation analysis had been used to examine the system's stability.From the spatial stability of the system,the conditions for Turing instability have been derived.The multiple-scale analysis has been used to derive the amplitude equations of the system.The stability analysis of these amplitude equations leads to the formation of Turing patterns.Finally,numerical simulations are used to analyze spatial patterns forming in 1-D and 2-D.The studies indicate that the model can generate a complex pattern structure and that self-diffusion has a drastic impacton species distribution. 展开更多
关键词 prey predator system hunting cooperation Allee effect HOPF-BIFURCATION diffusive instability amplitudeequation
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On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method 被引量:1
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作者 Kamal Shah Thabet Abdeljawad +1 位作者 Fahd Jarad Qasem Al-Mdallal 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第8期1457-1472,共16页
This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system.For the proposed study,we consider the model under the conformable fractional order derivative(CFOD).We investigate ... This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system.For the proposed study,we consider the model under the conformable fractional order derivative(CFOD).We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution.Indeed,Schauder and Banach fixed point theorems are utilized to prove our claim.Further,an algorithm for the approximate analytical solution to the proposed problem has been established.In this regard,the conformable fractional differential transform(CFDT)technique is used to compute the required results in the form of a series.Using Matlab-16,we simulate the series solution to illustrate our results graphically.Finally,a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given. 展开更多
关键词 prey predator model existence results conformable fractional differential transform
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THE MATHEMATICAL BEHAVIOR OF A NONAUTONOMOUS VOLTERRA PREDATOR-PREY SYSTEM WITH UNDERCROWDING EFFECT 被引量:1
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作者 王基琨 《Annals of Differential Equations》 1998年第2期209-214,共6页
This paper investigates a nonautonomous Volterra predator Prey system with undercrowding effect. A set of sufficient conditions for the existence and globally asymptotic stability of positive solution, which is easy t... This paper investigates a nonautonomous Volterra predator Prey system with undercrowding effect. A set of sufficient conditions for the existence and globally asymptotic stability of positive solution, which is easy to be verified, is obtained. 展开更多
关键词 Mathematical behavior undercrowding effect predator prey.
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Integrated search technique for parameter determination of SVM for speech recognition 被引量:2
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作者 Teena Mittal R.K.Sharma 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第6期1390-1398,共9页
Support vector machine(SVM)has a good application prospect for speech recognition problems;still optimum parameter selection is a vital issue for it.To improve the learning ability of SVM,a method for searching the op... Support vector machine(SVM)has a good application prospect for speech recognition problems;still optimum parameter selection is a vital issue for it.To improve the learning ability of SVM,a method for searching the optimal parameters based on integration of predator prey optimization(PPO)and Hooke-Jeeves method has been proposed.In PPO technique,population consists of prey and predator particles.The prey particles search the optimum solution and predator always attacks the global best prey particle.The solution obtained by PPO is further improved by applying Hooke-Jeeves method.Proposed method is applied to recognize isolated words in a Hindi speech database and also to recognize words in a benchmark database TI-20 in clean and noisy environment.A recognition rate of 81.5%for Hindi database and 92.2%for TI-20 database has been achieved using proposed technique. 展开更多
关键词 support vector machine (SVM) predator prey optimization speech recognition Mel-frequency cepstral coefficients wavelet packets Hooke-Jeeves method
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Global stability of a stochastic predator-prey model with Allee effect 被引量:4
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作者 Baodan Tian Liu Yang Shouming Zhong 《International Journal of Biomathematics》 2015年第4期37-51,共15页
In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial... In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings. 展开更多
关键词 predator prey model stochastic perturbation Allee effect It5 formula sta-bility.
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ANALYSIS OF A PREDATOR-PREY MODEL WITH DISEASE IN THE PREY 被引量:3
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作者 CHUNYANJI DAQING JIANG 《International Journal of Biomathematics》 2013年第3期11-31,共21页
In this paper, we discuss the behavior of a predator-prey model with disease in the prey with and without stochastic perturbation, respectively. First, we briefly give the dynamic of the deterministic system, by analy... In this paper, we discuss the behavior of a predator-prey model with disease in the prey with and without stochastic perturbation, respectively. First, we briefly give the dynamic of the deterministic system, by analyzing stabilities of its four equilibria. Then, we consider the asymptotic behavior of the stochastic system. By Lyapunov analysis methods, we show the stochastic stability and its long time behavior around the equi- librium of the deterministic system. We obtain there are similar properties between the stochastic system and its corresponding deterministic system, when white noise is small. But large white noise can make a unstable deterministic system to be stable. 展开更多
关键词 predator prey model with disease Ito formula STABLE stochastically unsta-ble stochastically stable in the large.
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GLOBAL ASYMPTOTIC STABILITY FOR A TWO-SPECIES DISCRETE RATIO-DEPENDENT PREDATOR-PREY SYSTEM 被引量:2
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作者 XIANGLAI ZHUO 《International Journal of Biomathematics》 2013年第1期53-68,共16页
The dynamical behaviors of a two-species discrete ratio-dependent predator-prey sys- tem are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization meth... The dynamical behaviors of a two-species discrete ratio-dependent predator-prey sys- tem are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization method. Further, we also obtain a new sufficient condition to ensure that the positive equilibrium is globally asymptotically stable by using an iteration scheme and the comparison principle of difference equations, which generalizes what paper [G. Chen, Z. Teng and Z. Hu, Analysis of stability for a discrete ratio-dependent predator-prey system, Indian J. Pure Appl. Math. 42(1) (2011) 1-26] has done. The method given in this paper is new and very resultful comparing with papers [H. F. Huo and W. T. Li, Existence and global stability of periodic solutions of a discrete predator--prey system with delays, Appl. Math. Comput. 153 (2004) 337-351; X. Liao, S. Zhou and Y. Chen, On permanence and global stability in a general Gilpin- Ayala competition predator prey discrete system, Appl. Math. Comput. 190 (2007) 500-509] and it can also be applied to study the global asymptotic stability for general multiple species discrete population systems. At the end of this paper, we present an open question. 展开更多
关键词 Discrete ratio-dependent predator prey system local stability variational matrix global stability iteration scheme method.
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Permanence of a diffusive Leslie-Gower predator-prey model incorporating a prey refuge 被引量:1
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作者 Wensheng Yang 《International Journal of Biomathematics》 2014年第3期73-80,共8页
The diffusive Leslie-Clower predator-prey model incorporating a prey refuge is recon- sidered here. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained, a... The diffusive Leslie-Clower predator-prey model incorporating a prey refuge is recon- sidered here. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained, and our results supplement earlier ones. 展开更多
关键词 Diffusive system LESLIE-GOWER PERMANENCE predator prey refuge.
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DYNAMICS OF A DIFFUSIVE PREDATOR-PREY MODEL WITH ADDITIVE ALLEE EFFECT 被引量:1
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作者 YONGLI CAI WEIMING WANG JINFENG WANG 《International Journal of Biomathematics》 2012年第2期105-115,共11页
In this paper, we investigate the dynamics of a diffusive predator prey model with Holling-II functional response and the additive Allee effect in prey. We show the local and global asymptotical stability of the posit... In this paper, we investigate the dynamics of a diffusive predator prey model with Holling-II functional response and the additive Allee effect in prey. We show the local and global asymptotical stability of the positive equilibrium, and give the conditions of the existence of the Hopf bifurcation. By carrying out global qualitative and bifurcation analysis, it is shown that the weak and strong Allee effects in prey can induce different dynamical behavior in the predator-prey model. Furthermore, we use some numerical simulations to illustrate the dynamics of the model. The results may be helpful for controlling and managing the predator-prey system. 展开更多
关键词 Allee effect predator prey model global stability Hopf bifurcation.
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Canard explosion,homoclinic and heteroclinic orbits in singularly perturbed generalist predator-prey systems
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作者 Ali Atabaigi 《International Journal of Biomathematics》 SCIE 2021年第1期151-174,共24页
This paper studies the dynamics of the generalist predator–prey systems modeled in[E.Alexandra,F.Lutscher and G.Seo,Bistability and limit cycles in generalist predator–prey dynamics,Ecol.Complex.14(2013)48–55].When... This paper studies the dynamics of the generalist predator–prey systems modeled in[E.Alexandra,F.Lutscher and G.Seo,Bistability and limit cycles in generalist predator–prey dynamics,Ecol.Complex.14(2013)48–55].When prey reproduces much faster than predator,by combining the normal form theory of slow-fast systems,the geometric singular perturbation theory and the results near non-hyperbolic points developed by Krupa and Szmolyan[Relaxation oscillation and canard explosion,J.Differential Equations174(2)(2001)312–368;Extending geometric singular perturbation theory to nonhyperbolic points—fold and canard points in two dimensions,SIAM J.Math.Anal.33(2)(2001)286–314],we provide a detailed mathematical analysis to show the existence of homoclinic orbits,heteroclinic orbits and canard limit cycles and relaxation oscillations bifurcating from the singular homoclinic cycles.Moreover,on global stability of the unique positive equilibrium,we provide some new results.Numerical simulations are also carried out to support the theoretical results. 展开更多
关键词 Canard cycle relaxation oscillation generalist predator prey singular perturbation HOMOCLINIC HETEROCLINIC
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Traveling wave solutions for a diffusive predator-prey model with predator saturation and competition
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作者 Lin Zhu Shi-Liang Wu 《International Journal of Biomathematics》 2017年第6期231-253,共23页
The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria: a zero equilibr... The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria: a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium. 展开更多
关键词 Diffusive predator prey model traveling wave solution shooting argument Wazewski's set LaSalle's invariance principle.
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BIFURCATION CONTROL OF A PREDATOR-PREY MODEL BASED ON NUTRITION KINETICS
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作者 LICHUN ZHAO JINGNA LIU WEI GAO 《International Journal of Biomathematics》 2013年第4期1-19,共19页
The existence conditions of Hopf bifurcation for a predator prey model based on nutri- tion kinetics are given. The two results may appear as follows: one is that the model has a stable periodic trajectory from Hopf ... The existence conditions of Hopf bifurcation for a predator prey model based on nutri- tion kinetics are given. The two results may appear as follows: one is that the model has a stable periodic trajectory from Hopf bifurcation, which shows the system is in an eco- logical balance; the other is that periodic trajectory from Hopf bifurcation is unstable, which indicates the system is in a sharp or catastrophic loss of stability. For the latter, a bifurcation controller is designed to make the periodic trajectory stable. Finally, some simulations are carried out to prove the results. 展开更多
关键词 Nutrition kinetics Hopf bifurcation bifurcation control predator prey model.
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