Predation fear and its carry-over effect in a fractional order prey-predator model with prey refuge

Balcı E.

CHAOS SOLITONS & FRACTALS, vol.175, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 175
  • Publication Date: 2023
  • Doi Number: 10.1016/j.chaos.2023.114016
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, zbMATH
  • Keywords: Caputo derivative, Carry-over effect, Fear effect, Hopf bifurcation, Prey refuge, Prey–predator
  • Erciyes University Affiliated: Yes


This research article centers on the formulation and analysis of a novel prey-predator model that integrates the impacts of predation fear, prey refuge, and carry-over effects. The model is formulated and analyzed using fractional differential equations (FDEs). The model incorporates ecological concepts such as anti -predator behaviours and memory effects to maintain a better understanding of prey-predator interactions. The mathematical model is developed based on a basic prey-predator model with a Michelis-Menten functional response and includes fear-induced carry-over effects, prey refuge, and fractional order derivatives. The study investigates the well-posedness, stability, and Hopf bifurcation of the proposed model and conducts detailed numerical investigations. The integration of different anti-predatory mechanisms and the use of FDEs contribute to a comprehensive understanding of the dynamics of prey-predator interactions and provide useful insights into the complexities of ecological systems.