Dynamical Behavior of Discrete Ratio-Dependent Predator-Prey System  

作　　者：Mingxia Duan Jiying Ma Mingxia Duan;Jiying Ma(Department of Mathematics, University of Shanghai for Science and Technology, Shanghai, China;College of Science, University of Shanghai for Science and Technology, Shanghai, China)

机构地区：[1]Department of Mathematics, University of Shanghai for Science and Technology, Shanghai, China [2]College of Science, University of Shanghai for Science and Technology, Shanghai, China

出　　处：《Open Journal of Applied Sciences》2023年第3期396-413,共18页应用科学（英文）

摘　　要：In this paper, we propose a discrete ratio-dependent predator-prey system. The stability of the fixed points of this model is studied. At the same time, it is shown that the discrete model undergoes fold bifurcation and flip bifurcation by using bifurcation theory and the method of approximation by a flow. Numerical simulations are presented not only to demonstrate the consistence with our theoretical analyses, but also to exhibit the complex dynamical behaviors, such as the cascade of period-doubling bifurcation in period-2 and the chaotic sets. The Maximum Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors. These results show that the direct discrete method has more rich dynamic behaviors than the discrete model obtained by Euler method.In this paper, we propose a discrete ratio-dependent predator-prey system. The stability of the fixed points of this model is studied. At the same time, it is shown that the discrete model undergoes fold bifurcation and flip bifurcation by using bifurcation theory and the method of approximation by a flow. Numerical simulations are presented not only to demonstrate the consistence with our theoretical analyses, but also to exhibit the complex dynamical behaviors, such as the cascade of period-doubling bifurcation in period-2 and the chaotic sets. The Maximum Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors. These results show that the direct discrete method has more rich dynamic behaviors than the discrete model obtained by Euler method.

关 键 词：Discrete-Time Predator-Prey System Ratio-Dependent Functional Response Stability and Bifurcation Analysis 

分 类 号：O17[理学—数学]