Effect of hunting cooperation and fear in a predator-prey model

Pal, Saheb ; Pal, Nikhil ; Samanta, Sudip ; Chattopadhyay, Joydev (2019) Effect of hunting cooperation and fear in a predator-prey model Ecological Complexity, 39 . p. 100770. ISSN 1476945X

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Official URL: http://doi.org/10.1016/j.ecocom.2019.100770

Related URL: http://dx.doi.org/10.1016/j.ecocom.2019.100770

Abstract

Dynamics of predator-prey systems under the influence of cooperative hunting among predators and the fear thus imposed on the prey population is of great importance from ecological point of view. The role of hunting cooperation and the fear effect in the predator-prey system is gaining considerable attention by the researchers recently. But the study on combined effect of hunting cooperation and fear in the predator-prey system is not yet studied. In the present paper, we investigate the impact of hunting cooperation among predators and predator induced fear in prey population by using the classical predator-prey model. We consider that predator populations cooperate during hunting. We also consider that hunting cooperation induces fear among prey, which has far richer and complex dynamics. We observe that without hunting cooperation, the unique coexistence equilibrium point is globally asymptotically stable. However, an increase in the hunting cooperation induced fear may destabilize the system and produce periodic solution via Hopf-bifurcation. The stability of the Hopf-bifurcating periodic solution is obtained by computing the Lyapunov coefficient. The limit cycles thus obtained may be supercritical or subcritical. We also observe that the system undergoes the Bogdanov-Takens bifurcation in two-parameter space. Further, we observe that the system exhibits backward bifurcation between predator-free equilibrium and coexisting equilibrium. The system also exhibits two different types of bi-stabilities due to subcritical Hopf-bifurcation (between interior equilibrium and stable limit cycle) and backward bifurcation (between predator-free and interior equilibrium points). Further, we observe strong demographic Allee phenomenon in the system. To visualize the dynamical behavior of the system, extensive numerical experiments are performed by using MATLAB and MATCONT softwares.

Item Type:Article
Source:Copyright of this article belongs to Elsevier B.V
ID Code:132181
Deposited On:14 Dec 2022 09:18
Last Modified:14 Dec 2022 09:18

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