Complex dynamics in a two species system with Crowley–Martin response function: Role of cooperation, additional food and seasonal perturbations

Bapin Mondal, Ashraf Adnan Thirthar, Nazmul Sk, Manar A. Alqudah, Thabet Abdeljawad*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This research article investigates the interaction between prey and a generalist predator, considering the effect of hunting cooperation. The predator–prey interaction is modeled using a predator dependent functional response, specifically the Crowley–Martin type. System's dynamics are explored using both analytical and numerical techniques. Feasible equilibria are analyzed, and their local stability is determined. Various bifurcations in the system are explored, and one-and two-parameter bifurcation structures are constructed to unveil complex dynamical behaviors. Our findings reveal that both prey and predator face extinction when the predator growth rate from alternative food sources exceeds certain threshold values. However, prey extinction is driven by the higher levels of hunting cooperation among predators, while the availability of external food sources enhances the system's stability and persistence. Furthermore, we enhance the model by introducing seasonal perturbations, acknowledging the influence of seasonal variations on ecological parameters. The system exhibits diverse patterns in response to seasonality, contributing to a deeper understanding of the dynamics in predator–prey interactions.

Original languageEnglish
Pages (from-to)415-434
Number of pages20
JournalMathematics and Computers in Simulation
Volume221
DOIs
Publication statusPublished - Jan 2024
Externally publishedYes

Keywords

  • Bifurcations
  • Bistability
  • Bursting
  • Generalist predator
  • Hunting cooperation
  • Seasonal perturbation

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