Multiple Bifurcations in a Discrete Bazykin Predator–Prey Model with Predator Intraspecific Interactions and Ratio-Dependent Functional Response

Dongpo Hu ^[1] ; Xiao Yu ^[1] ; Zhaowen Zheng ^[2] ; Chuan Zhang ^[1] ; Ming Liu ^[1]
1. [1] Qufu Normal University
  
  Qufu Normal University
  
  China
2. [2] Guangdong Polytechnic Normal University
  
  Guangdong Polytechnic Normal University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
Idioma: inglés
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Resumen
- A discrete Bazykin predator–prey model with predator intraspecific interactions and ratio-dependent functional response is proposed and investigated. A brief mathematical analysis of the model involves giving fixed points and analyzing local stability.
  
  Codimension-one bifurcations such as the transcritical, fold, flip, Neimark-Sacker bifurcations and codimension-two bifurcations, including the fold-flip bifurcation, 1:2, 1:3, and 1:4 strong resonances, are investigated. Accurate theoretical analysis and exquisite numerical simulation are given simultaneously, which support the main content of this manuscript. With the help of several local attraction basins, period, and Lyapunov exponent diagrams, an intriguing set of fascinating dynamics in the two-parameter spaces of integral step size with other parameters is uncovered. The results in this paper reveal that the dynamics of the discrete-time predator–prey system in both single-parameter and two-parameter spaces are inherently rich and complex.