TY - JOUR
T1 - Complex dynamics in a two species system with Crowley–Martin response function
T2 - Role of cooperation, additional food and seasonal perturbations
AU - Mondal, Bapin
AU - Thirthar, Ashraf Adnan
AU - Sk, Nazmul
AU - Alqudah, Manar A.
AU - Abdeljawad, Thabet
N1 - Publisher Copyright:
© 2024 International Association for Mathematics and Computers in Simulation (IMACS)
PY - 2024/7
Y1 - 2024/7
N2 - 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.
AB - 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.
KW - Bifurcations
KW - Bistability
KW - Bursting
KW - Generalist predator
KW - Hunting cooperation
KW - Seasonal perturbation
UR - http://www.scopus.com/inward/record.url?scp=85188140477&partnerID=8YFLogxK
U2 - 10.1016/j.matcom.2024.03.015
DO - 10.1016/j.matcom.2024.03.015
M3 - Article
AN - SCOPUS:85188140477
SN - 0378-4754
VL - 221
SP - 415
EP - 434
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -