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Dynamics of a predator-prey system with sublethal effects of pesticides on pests and natural enemies

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International Journal of Biomathematics 2024年第1期17卷 151-175页

作者： Xiangjun Dai Jianjun Jiao Qi Quan Airen Zhou School of Mathematical Sciences Guizhou Normal University Guiyang 550025P.R.China School of Mathematics and Statistics Guizhou University of Finance and Economics Guiyang 550025 P.R.China School of Date Science Tongren University Tongren 554300P.R.China

Considering the influence of sublethal concentration of pesticides on pests and natural enemies,we propose a pest-management model with impulsive effect on chemical control and biological control strategies periodic spraying pesticide and releasing predatory natural enemies.By using the Floquet theory and the comparison theorem of impulsive differential equations,a sufficient condition for the global asymptotic stability of the pest-eradication periodic solution is obtained.The persistence of the system is further studied,and a sufficient condition for the persistence of the system is obtained.Finally,some numerical simulations are shown to verify our theoretical works.Our works indicate that the sublethal effects of insecticides and the release of predatory natural enemies play significant roles in pest control in agricultural production.

关键词： predator-prey system sublethal effect global asymptotic stability permanence

Global Stability of a predator-prey system with Stage Structure for the predator

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Acta Mathematica Sinica,English Series 2004年第1期20卷 63-70页

作者： YanNiXIAO LanSunCHEN DepartmentofmathematicalSciences TheUniversityofLiverpoolLiverpoolL697ZLUK AcademyofMathematics&systemSciences ChineseAcademyofScienceBeijing100080.P.R.china

In this paper, some feasibly suffcient conditions are obtained for the global asymptotic stability of a positive steady state of a predator-prey system with stage structure for the predator by using the theory of comp... 详细信息

关键词： Global stability predator-prey system Competitive systems Stage structure

Dynamics and response reshaping of nonlinear predator-prey system undergoing random abrupt disturbances

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Applied Mathematics and Mechanics(English Edition) 2021年第8期42卷 1123-1134页

作者： Lei XIA Jiaojiao SUN Zuguang YING Ronghua HUAN Weiqiu ZHU Department of Mechanics Key Laboratory of Soft Machines and Smart Devices of Zhejiang ProvinceZhejiang UniversityHangzhou 310027China

An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.

关键词： random excitation nonlinear dynamics reshaping control stationary probability density function(SPDF) predator-prey system

Permanence and periodic solutions of delayed predator-prey system with impulse

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Applied Mathematics(A Journal of Chinese Universities) 2010年第3期25卷 264-276页

作者： SHI Hong-bo School of Mathematical Sciences Huaiyin Normal University Jiangsu 223300 China

The existence of positive periodic solution of a generalized semi-ratio-dependent predator-prey system with time delay and impulse is studied by using the continuation theorem based on the coincidence degree theory. T... 详细信息

关键词： predator-prey system impulse periodic solution permanence coincidence degree.

Complex Dynamics in a Discrete-time predator-prey system without Allee Effect

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 355-376页

作者： Xian-wei CHEN Xiang-ling FU ZHU-JUN JING School of Mathematics and Computational Science Hunan University of Science and Technology Department of Mathematics Hunan Normal University Academy of Mathematics and systems Science Chinese Academy of Sciences

In this paper, complex dynamics of the discrete-time predator-prey system without Allee effect are investigated in detail. Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory and checked up by numerical simulations. Chaos, in the sense of Marotto, is also proved by both analytical and numerical methods. Numerical simulations included bifurcation diagrams, Lyapunov exponents, phase portraits, fractal dimensions display new and richer dynamics behaviors. More specifically, this paper presents the finding of period-one orbit, period-three orbits, and chaos in the sense of Marotto, complete period-doubling bifurcation and invariant circle leading to chaos with a great abundance period-windows, simultaneous occurrance of two different routes （invariant circle and inverse period- doubling bifurcation, and period-doubling bifurcation and inverse period-doubling bifurcation） to chaos for a given bifurcation parameter, period doubling bifurcation with period-three orbits to chaos, suddenly appearing or disappearing chaos, different kind of interior crisis, nice chaotic attractors, coexisting （2,3,4） chaotic sets, non-attracting chaotic set, and so on, in the discrete-time predator-prey system. Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding is given of the discrete-time predator-prey systems with Allee effect and without Allee effect.

关键词： predator-prey system flip bifurcation Hopf bifurcation Marotto＇s chaos transient chaos

On the predator-prey system with Holling-(n+1)Functional Response

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Acta Mathematica Sinica,English Series 2007年第1期23卷 1-6页

作者： Wei WANG Jian Hua SUN Department of Mathematics Nanjing University Nanying 210008 P. R. China

The qualitative properties of a predatorprey system with Holling-（n ＋ 1） functional response and a fairly general growth rate are completely investigated. The necessary and sufficient condition to guarantee the uni... 详细信息

关键词： predator-prey system Limit cycle Uniqueness Dulac function

POSITIVE STEADY STATES AND DYNAMICS FOR A DIFFUSIVE predator-prey system WITH A DEGENERACY

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Acta Mathematica Scientia 2016年第2期36卷 537-548页

作者：杨璐张贻民 School of Mathematics and Statistics Lanzhou University Lanzhou 730000 China Key Laboratory of Applied Mathematics and Complex systems Gansu 730000 China Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan 430071 China

In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by the degeneracy of the intra-specific pressures for the prey. By the bifurcation method, the degree theory, and a priori estimates, we discuss the existence and multiplicity of positive steady states. Moreover, by the comparison argument, we also discuss the dynamical behavior for the diffusive predator-prey system.

关键词： predator-prey system steady state solution dynamical behavior

Dynamics in a Discrete-time predator-prey system with Allee Effect

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Acta Mathematicae Applicatae Sinica 2013年第1期29卷 143-164页

作者： Xian-wei Chen Xiang-ling Fu Zhu-jun Jing Department of Mathematics Hunan Normal University School of Mathematics and Computational Science Hunan University of Science and Technology Academy of Mathematics and systems Science Chinese Academy of Sciences

In this paper, dynamics of the discrete-time predator-prey system with Allee effect are investigated in detail. Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory, and then further illustrated by numerical simulations. Chaos in the sense of Marotto is proved by both analytical and numerical methods. Numerical simulations included bifurcation diagrams, Lyapunov exponents, phase portraits, fractal dimensions display new and rich dynamical behavior. More specifically, apart from stable dynamics, this paper presents the finding of chaos in the sense of Marotto together with a host of interesting phenomena connected to it. The analytic results and numerical simulations demostrates that the Allee constant plays a very important role for dynamical behavior. The dynamical behavior can move from complex instable states to stable states as the Allee constant increases （within a limited value）. Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding of the discrete-time predator-prey with Allee effect is given.

关键词： predator-prey system Allee effect flip bifurcation Hopf bifurcation Marotto＇s chaos transientchaos invariant circle periodic window

PERSISTENCE IN A THREE SPECIES LOTKA-VOLTERRA NONPERIODIC predator-prey system

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Applied Mathematics and Mechanics(English Edition) 2000年第8期21卷 879-884页

作者：张银萍孙继涛 Institute of Applied Mathematics Shanghai Railway University Shanghai P R China

The predator-prey model for three species in which the right-hand sides are nonperiodic functions in time were considered, It's proved that the model is persistent under appropriate conditions.

关键词： persistence predator-prey system nonperiodic