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 ...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.展开更多
运用多尺度法研究了一类van der Pol-Duffing系统的Hopf分岔问题和分岔控制问题.首先,分析了自治的van der Pol-Duffin g系统的Hopf分岔问题,并设计了线性和非线性联合的状态反馈控制器,对其进行了Hopf分岔控制.然后,设计了线性时滞参数...运用多尺度法研究了一类van der Pol-Duffing系统的Hopf分岔问题和分岔控制问题.首先,分析了自治的van der Pol-Duffin g系统的Hopf分岔问题,并设计了线性和非线性联合的状态反馈控制器,对其进行了Hopf分岔控制.然后,设计了线性时滞参数,对非自治时滞反馈系统的主共振分岔响应进行了控制.研究结果表明,适当选取参数不仅可以改变分岔响应曲线的拓扑形态,还可以改变分岔点的位置.展开更多
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...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.展开更多
基金Supported by the Anhui Provincial Department of National Land and Resources with their Science and Technology Project entitled "Research on a Dynamic Monitoring Land Usage,Evaluation and Decision Support Management System in Wanjiang Demonstration Area"(Grant No.2011-K-23)Anhui Agricultural University,China(Grant No.YJ2012-03,No.XK2013029 and No.11201002)The Natural Sciences and Engineering Research Council of Canada
文摘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.
基金Supported by the Natural Science Foundation(No.11ZB192)of Sichuan Education Bureauthe key program of Science and Technology Foundation(No.11Zd1007)of Southwest University of Science and Technology
文摘运用多尺度法研究了一类van der Pol-Duffing系统的Hopf分岔问题和分岔控制问题.首先,分析了自治的van der Pol-Duffin g系统的Hopf分岔问题,并设计了线性和非线性联合的状态反馈控制器,对其进行了Hopf分岔控制.然后,设计了线性时滞参数,对非自治时滞反馈系统的主共振分岔响应进行了控制.研究结果表明,适当选取参数不仅可以改变分岔响应曲线的拓扑形态,还可以改变分岔点的位置.
文摘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.
