BIFURCATION ANALYSIS OF A DISCRETE PREDATOR–PREY MODEL WITH FEAR EFFECTS, PREY REFUGE, HARVESTING AND CROWLEY–MARTIN FUNCTIONS
Abstract
In this paper, we consider a discrete predator–prey model with fear effects, prey refuge, harvesting and Crowley–Martin functional responses. First, we analyze the existence of the model’s fixed points. Subsequently, we apply bifurcation theory to establish the conditions for the occurrence of codimension-two bifurcations, including fold-flip bifurcation, 1:1 strong resonance and 1:2 strong resonance. Finally, we verify our theoretical analysis through numerical simulations, presenting bifurcation diagrams, maximum Lyapunov exponents diagrams, phase portraits and the two-parameter spaces under the specified initial conditions.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Advanced Differential Equations and Dynamical Systems
Ecosystem dynamics and resilience
Publication details
- Journal / source
- Journal of Biological Systems
- Volume
- 34
- Issue
- 03
- Pages
- 399–427
- Publication date
- 30 January 2026
- Language
- EN