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Stability and Hopf Bifurcation Analysis of a Predator-Prey Model with Time Delayed Incomplete Trophic Transfer

Acta Mathematicae Applicatae Sinica 2015年第1期31卷 235-246页

作者： Chang-qin ZHANG Liping LIU Ping YAN Lin-zhong ZHANG School of Sciences Anhui Agricultural University Department of Mathematics Lakehead University

A new nonlinear predator-prey model with incomplete trophic transfer is introduced. In this model, we assume that the rate of the trophic absorption of the predator is less than the rate of the conversion of consumed prey to predator in the Ivlev-type functional responses. The existence and uniqueness of the positive equilibrium of the model and the stability of the equilibrium of the model are studied under various conditions. Hopf bifurcation analysis of the delayed model is provided.

关键词： incomplete trophic transfer time delay Ivlev-type existence and uniqueness stability hopfbifurcation

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Backward,Hopf bifurcation in a heroin epidemic model with treat age

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第2期12卷 198-222页

作者： Soufiane Bentout Salih Djilali Behzad Ghanbari Laboratoire d’Analyse Non Lin´eaire et Math´ematiques Appliqu´ees Universit´e de Tlemcen TlemcenAlgeria Department of Basic Science Kermanshah University of Technology KermanshahIran Faculty of Exact and Computer Sciences Mathematic Department Hassiba Benbouali UniversityChlefAlgeria §Department of Mathematics and Informatics Belhadj Bouchaib University Center of Ain Temouchent BP 284 RP 46000Algeria

Heroin is considered as damage on the health of the *** this paper,we consider a heroin epidemic model with treat age,where the inner rivalry in between the drug users for a small dose of drugs is *** influence of treatment period for a drug consumer before quitting treatment is investigated,where it is obtained that the considered model can undergo backward bifurcation,which shows the possibility of having two endemic equilibriums,this type of bifurcation is discussed in terms of the basic reproduction number *** bifurcation diagram is drown in the case of an age structured ***,we show the existence of Hopf bifurcation is shown under suitable conditions on the model *** obtained mathematical results are confirmed numerically.

关键词： Backward bifurcation heroin epidemic age-structured model hopfbifurcation

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Under the influence of crowding effects:Stability,bifurcation and chaos control for a discrete-time predator-prey model

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International Journal of Biomathematics 2019年第4期12卷 185-213页

作者： Muhammad Aqib Abbasi Qamar Din Department of Mathematics University of the Poonch Rawalakot Pakistan

The interaction between predators and preys exhibits more complicated behavior under the influence of crowding effects. By taking into account the crowding effects, the qualitative behavior of a prey-predator model is investigated. Particularly, we examine the boundedness as well as existence and uniqueness of positive steady-state and stability analysis of the unique positive steady-state. Moreover, it is also proved that the system undergoes Hopf bifurcation and flip bifurcation with the help of bifurcation theory. Moreover, a chaos control technique is proposed for controlling chaos under the influence of bifurcations. Finally, numerical simulations are provided to illustrate the theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The presence of chaotic behavior in the model is confirmed by computing maximum Lyapunov exponents.

关键词： Prey-predator model stability analysis boundedness flip bifurcation hopfbifurcation chaos control

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