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Hopf bifurcation and chaos in a Leslie–Gower prey–predator model with discrete delays

International Journal of Biomathematics 2020年第6期13卷 135-161页

作者： Anuraj Singh Preeti Pradeep Malik ABV-Indian Institute of Information Technology and Management Gwalior M.P.India Department of Mathematics University of Petroleum Energy Studies DehradunUttarakhandIndia

In this work,a Leslie–Gower prey-predator model with two discrete delays has been *** positivity,boundedness and persistence of the delayed system have been *** system exhibits the phenomenon of Hopf bifurcation with respect to both *** conditions for occurrence of Hopf bifurcation are obtained for different combinations of *** is shown that delay induces the complexity in the system and brings the periodic oscillations,quasi-periodic oscillations and *** properties of periodic solution have been determined using central manifold and normal form ***,the global stability of the system has been established for different cases of discrete *** numerical computation has also been performed to verify analytical results.

关键词： discrete delays limit cycle global stability Hopf bifurcation chaotic behavior

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Periodic Solutions for a Class of Neutral Functional Differential Equations with Distributed and discrete delays

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Chinese Quarterly Journal of Mathematics 2012年第4期27卷 485-494页

作者：周宗福曾力贾宝瑞徐建中 School of Mathematical Sciences Anhui University

Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover,we construct an example to illustrate the feasibility of our results.

关键词： neutral functional differential equation infinite distributed delay discrete delays Krasnoselskii’s fixed point theorem periodic solutions

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PERMANENCE AND GLOBAL ATTRACTIVITY OF N-SPECIES COOPERATION SYSTEM WITH discrete TIME delays AND FEEDBACK CONTROLS

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Annals of Differential Equations 2007年第1期23卷 18-25页

作者： He Weilian College of Basic Medicine Fujian Medical University Fuzhou 350004

In this paper, we consider the N-species cooperation system with discrete time delays and feedback controls. By using the differential inequality theory and constructing a suitable Lyapunov functional, we obtain suffi... 详细信息

关键词： cooperation system permanence global attractivity discrete delays feedback controls

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Global stability for multi-species Lotka-Volterra cooperative systems： One hyper-connected mutualistic-species

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International Journal of Biomathematics 2015年第3期8卷 215-223页

作者： Cruz Vargas-De-Leon Unidad de Medicina Experimental Hospital General de Mexico"Dr. Eduardo Liceaga" DF 06726 Mexico

We propose two models of one hyper-connected mutualistic-species described by delay differential equations of Lotka-Volterra type. An hyper-connected model comprises a central species interacting with a number of peripheral species around it, that is to say, one animal species （pollinators or dispersers） that interacts with several plant species （flowering plants or fruit trees）, or several animal species that interact with one plant species. We derive a necessary and sufficient condition for the global asymptotic stability of the unique coexisting steady state of hyper-connected systems by means of novel Lyapunov functionals.

关键词： Lotka Volterra cooperative system discrete delays distributed delays Lyapunov functional global stability.

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