TY - JOUR
T1 - Bistability and tristability in a deterministic prey–predator model
T2 - Transitions and emergent patterns in its stochastic counterpart
AU - Sk, Nazmul
AU - Mondal, Bapin
AU - Thirthar, Ashraf Adnan
AU - Alqudah, Manar A.
AU - Abdeljawad, Thabet
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2023/11
Y1 - 2023/11
N2 - The paper focuses on studying the global dynamics of a simple prey–predator model. The model incorporates cooperative hunting behavior among predators and takes into account the effect of harvesting on the predator population. The interaction between the prey and predator follows the Crowley–Martin functional response. The study involves analyzing the equilibrium points of the system and investigating their stability properties through mathematical analysis. Various types of bifurcations, including Hopf bifurcation, saddle–node bifurcation, and transcritical bifurcation, are numerically demonstrated in the figures, highlighting the dynamic behavior of the model. One of the intriguing findings of the study is the occurrence of bistability and tristability in the model. To incorporate stochasticity into the model, white noise is added to the deterministic system. This allows for the examination of transitions between different steady states in the stochastic system. We have conducted an analysis of species persistence and extinction in relation to the presence of noise. The paper presents the stochastic sensitivity function (SSF) technique and the use of confidence ellipses to assess the likelihood of such transitions occurring in the system. Overall, the study provides insights into the complex dynamics of prey–predator interactions, considering factors such as cooperation, harvesting, and stochasticity. The results contribute to our understanding of population dynamics and the potential effects of environmental and human-induced perturbations on ecosystem stability.
AB - The paper focuses on studying the global dynamics of a simple prey–predator model. The model incorporates cooperative hunting behavior among predators and takes into account the effect of harvesting on the predator population. The interaction between the prey and predator follows the Crowley–Martin functional response. The study involves analyzing the equilibrium points of the system and investigating their stability properties through mathematical analysis. Various types of bifurcations, including Hopf bifurcation, saddle–node bifurcation, and transcritical bifurcation, are numerically demonstrated in the figures, highlighting the dynamic behavior of the model. One of the intriguing findings of the study is the occurrence of bistability and tristability in the model. To incorporate stochasticity into the model, white noise is added to the deterministic system. This allows for the examination of transitions between different steady states in the stochastic system. We have conducted an analysis of species persistence and extinction in relation to the presence of noise. The paper presents the stochastic sensitivity function (SSF) technique and the use of confidence ellipses to assess the likelihood of such transitions occurring in the system. Overall, the study provides insights into the complex dynamics of prey–predator interactions, considering factors such as cooperation, harvesting, and stochasticity. The results contribute to our understanding of population dynamics and the potential effects of environmental and human-induced perturbations on ecosystem stability.
KW - Confidence ellipse
KW - Cooperation
KW - Harvesting
KW - Noise
KW - Transition
KW - Tristability
UR - http://www.scopus.com/inward/record.url?scp=85172103026&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2023.114073
DO - 10.1016/j.chaos.2023.114073
M3 - Article
AN - SCOPUS:85172103026
SN - 0960-0779
VL - 176
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 114073
ER -