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Chaos control in a discrete-time predator-prey model with weak allee effect

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International Journal of Biomathematics 2018年第7期11卷 123-148页

作者： Saheb Pal Sourav Kumar Sasmal Nikhil Pal Department of Mathematics Visva-Bharati Santiniketan 731235India Department of Physics and Mathematics Aoyama Gakuin University Kanagawa 252-5258Japan

The stability of the predator-prey model subject to the allee effect is an interesting topic in recent *** this paper,we investigate the impact of weak allee effect on the stability of a discrete-time predator-prey model with Holling type-IV functional *** mathematical features of the proposed model are analyzed with the help of equilibrium analysis,stability analysis,and bifurcation *** provide sufficient conditions for the flip bifurcation by considering allee parameter as the bifurcation *** observe that the model becomes stable from chaotic dynamics as the allee parameter ***,we observe bi-stability behavior of the model between only prey existence equilibrium and the coexistence *** analytical findings are illustrated through numerical simulations.

关键词： Chaos control allee effect flip bifurcation bi-stability Lyapunov exponent

A study of stability and bifurcation analysis in discrete-time predator—prey system involving the allee effect

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International Journal of Biomathematics 2019年第1期12卷 255-269页

作者： Seval Isik Department of Mathematics and Science Education Faculty of Education Sivas Cumhuriyet University Sivas 58140Turkey

This paper deals with a discrete-time predator-prey system which is subject to an allee effect on *** investigate the existence and uniqueness and find parametric conditions for local asymptotic stability of fixed points of the discrete dynamic ***,using bifurcation theory,it is shown that the system undergoes Neimark-Sacker bifurcation in a small neighborhood of the unique positive fixed point and an inv aria nt circle will *** the direction of bifurcation is ***,numerical analysis is provided to illustrate the theoretical discussions with the help of Matlab ***,the main theoretical results are supported with numerical simulations.

关键词： Predator-Prey system fixed point stability Neimark-Sacker bifurcation allee effect

THE QUALITATIVE ANALYSIS OF A TWO SPECIES AMENSALISM MODEL WITH NON-MONOTONIC FUNCTIONAL RESPONSE AND allee EFFECT ON SECOND SPECIES

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Annals of Applied Mathematics 2019年第2期35卷 126-138页

作者： Xinyu Guan Hang Deng College of Math.and Computer Science Fuzhou University

In this paper, we present a two species amensalism model with non-monotonic functional response and allee effect on second species. Local and global stability of the boundary and interior equilibrium are investigated. By introducing the allee effect, we show that the boundary equilibrium have changed from unstable node and saddle into saddle-node. Also, the system subject to an allee effect has increased the time of reach to its stable steady-state solution, but has no influence on the final density of the two species. Our results are supported by numeric simulations.

关键词： amensalism model allee effect non-monotonic functional response global stability

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The Dynamical Behavior of a Predator-Prey System with Holling Type II Functional Response and allee Effect

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Applied Mathematics 2020年第5期11卷 407-425页

作者： Shuangte Wang Hengguo Yu Chuanjun Dai Min Zhao College of Mathematics and Physics Wenzhou University Wenzhou China Key Laboratory for Subtropical Oceans & Lakes Environment & Biological Resources Utilization Technology of Zhejiang Wenzhou University Wenzhou China School of Life and Environmental Science Wenzhou University Wenzhou China

In this paper, we mainly considered the dynamical behavior of a predator-prey system with Holling type II functional response and allee-like effect on predator, including stability analysis of equilibria and Hopf bifurcation. Firstly, we gave some sufficient conditions to guarantee the existence, the local and global stability of equilibria as well as non-existence of limit cycles. By using the cobweb model, some cases about the existence of interior equilibrium are also illustrated with numerical outcomes. These existence and stability conclusions of interior equilibrium are also suitable in corresponding homogeneous reaction-diffusion system subject to the Neumann boundary conditions. Secondly, we theoretically deduced that our system has saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation under certain conditions. Finally, for the Hopf bifurcation, we choose d as the bifurcation parameter and presented some numerical simulations to verify feasibility and effectiveness of the theoretical derivation corresponding to the existence of yk, respectively. The Hopf bifurcations are supercritical and limit cycles generated by the critical points are stable.

关键词： Predator-Prey System Holling Type II Functional Response allee Effect Stability Hopf Bifurcation

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一类具有allee影响的捕食与被捕食模型

数学的实践与认识 2008年第10期38卷 136-140页

作者：王静薛亚奎中北大学数学系山西太原030051

分析并建立了具有allee影响的捕食与被捕食模型,被捕食者由于自身繁殖或是被捕食而具有了allee效应,分别讨论了强allee和弱allee对被捕食种群的影响,讨论了解的有界性和各平衡点的存在性,并证明了各平衡点的局部渐近稳定性,进一步通过... 详细信息

分析并建立了具有allee影响的捕食与被捕食模型,被捕食者由于自身繁殖或是被捕食而具有了allee效应,分别讨论了强allee和弱allee对被捕食种群的影响,讨论了解的有界性和各平衡点的存在性,并证明了各平衡点的局部渐近稳定性,进一步通过构造适当的Lyapunov函数分析了正平衡点E*的全局渐近稳定性.

关键词： allee 捕食-被捕食模型渐近稳定全局稳定

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污染环境下具有强allee效应的食饵-捕食系统收获策略

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广西民族大学学报（自然科学版） 2023年第1期29卷 72-81页

作者：钟颖韦煜明彭华勤广西师范大学数学与统计学院广西桂林541006

研究了外界环境被污染的情况下,具有allee效应和Holling-Ⅱ型功能反应函数的食饵-捕食模型的收获策略。首先讨论了该系统平衡点的稳定性,其次利用Liapunov函数证明了正平衡点的全局稳定性,然后讨论系统的生物经济平衡的存在性,用Pontrya... 详细信息

研究了外界环境被污染的情况下,具有allee效应和Holling-Ⅱ型功能反应函数的食饵-捕食模型的收获策略。首先讨论了该系统平衡点的稳定性,其次利用Liapunov函数证明了正平衡点的全局稳定性,然后讨论系统的生物经济平衡的存在性,用Pontryagin's最大值原理探讨了最优收获策略,最后利用数值模拟解释这些结果。

关键词：食饵-捕食系统毒物 allee Holling-Ⅱ型最优收获策略

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Intraseasonal asynchrony as a factor boosting isolation within a metapopulation: The case of the clouded apollo

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Insect Science 2019年第5期26卷 911-922页

作者： Pawet Adamski Adam M.Cmiel Anna M.Lipinska Polish Academy of Sciences Institute of Nature ConservationKrakowPoland

This article discusses the influence of phenology-related intraseasonal asynchrony on metapopulation dynamics and stability. As the part played by intraseasonal asynchrony is as yet unclear and poorly described, greater account of it should be taken in both metapopulation research and conservation practice. The subpopulations of the Parnassius mnemosyne metapopulation studied here are strongly isolated because of the phenological shift between them, despite the relatively small physical distances between them. This isolation is the result of a significant temporal shift in the species' flight periods in the main metapopulation centers: in som e seasons its flight times in the different subpopulations did not overlap at all. The predicted results of such strong intraseasonal asynchrony are not altogether clear. On the one hand, they reduce the vulnerability of the entire metapopulation to the effects of short-term random disasters. On the other, the ever-greater isolation of subpopulations may cause the metapopulation to becom e a nonequilibrium one, which will have a serious impact on its long-term survival.

关键词： allee effect demography mathematical modeling metapopulation stability phenology

Analysis of a predator-prey model with herd behavior and disease in prey incorporating prey refuge

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International Journal of Biomathematics 2019年第1期12卷 133-171页

作者： Sangeeta Saha G.P.Samanta Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur Howrah-711103India

In this work,we have introduced an eco-epidemiological model of an infected predator prey *** of prey refuge gives that a fraction of the infected prey is available to the predator for ***,to make the model more realistic to the environment,we have introduced strong allee effect in the susceptible *** and positivity of the solution have been *** stability conditions of the equilibrium points have been found with the help of Routh-Hurwitz criterion and it has been observed that if a prey population is infected with a lethal disease,then both the prey(susceptible and infected)and predator cannot survive simultaneously in the system for any parametric *** disease transmission rate and the attack rate on the susceptible have an important role to control the system *** different values of these two key parameters,we have got only healthy or disease-free or predation-free or a fluctuating disease-free or even a fluctuating predator-free system with some certain parametric conditions.

关键词： allee effect herd behavior infected prey refuge extinction bifurcations

Modelling Large Scale Invasion of <i>Aedes aegypti </i>and <i>Aedes albopictus</i>Mosquitoes

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Advances in Pure Mathematics 2018年第3期8卷 245-265页

作者： Wenkui He Otto Richter Institute of Geoecology Technical University of Braunschweig Braunschweig Germany Dr. Knoell Consult GmbH Mannheim Germany

The principle aim of this work is to simulate the invasion of two invasive mosquito species Aedes aegypti and Aedes albopictus in central Europe at a landscape scale. The spatial-temporal dynamics of invasion is investigated in dependence of predation pressure, seasonal variation of ambient temperature as well as human population density. The introduction of temperature dependent entomological parameters enables the simulation of seasonal pattern of population dynamics. The influence of temperature, predation pressure and human population density on invasion is studied in one-dimensional cases. In two dimensions, georeferenced parameters such as annual mean temperature and human population density are prepared by a geographical information system and introduced into the finite element tool COMSOL Multiphysics. The results show that under the current temperature, central Europe cannot become a permanent breeding region for Aedes aegypti. However, southwest Germany especially the regions along the Upper Rhine Valley may provide suitable habitats for the permanent establishment of Aedes albopictus. An annual temperature rise of two degrees would lead to dramatic increase of invasion speed and extension range of Aedes albopictus.

关键词： Reaction-Diffusion Equations allee Effect Range Expansion Travelling Waves Temperature Dependence