Xiao, D.M. and Jennings, L.S. (2005) Bifurcations of a Ratio-Dependent Predator-Prey System with Constant Rate Harvesting. SIAM Journal on Applied Mathematics, 65, 737-753.
https://doi.org/10.1137/S0036139903428719

has been cited by the following article:

• TITLE: Dynamical Behavior of Discrete Ratio-Dependent Predator-Prey System

  AUTHORS: Mingxia Duan, Jiying Ma

  KEYWORDS: Discrete-Time Predator-Prey System, Ratio-Dependent Functional Response, Stability and Bifurcation Analysis

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.13 No.3, March 28, 2023

  ABSTRACT: 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.