Abstract
Some recent studies and field experiments show that predators affect their prey not only by direct capture; they also induce fear in prey species, which reduces their reproduction rate. Considering this fact, we propose a mathematical model to study the fear effect of a middle predator on its prey in a three-species food web system with harvesting. The ecological feasibility of solutions to the proposed system is guaranteed in terms of positivity and boundedness. The local stability of stationary points in the proposed system is derived. Multiple co-existing stationary points for the proposed system are observed, which makes the problem more interesting compared to the similar models studied previously. The local existence of periodic solutions through Hopf bifurcations is additionally secured numerically in the case of both unique and multiple coexisting stationary points. It is also observed that the system can exhibit strange attractors in the form of chaos. A detailed numerical simulation is performed to ensure the existence of periodic solutions and period- doubling routes to chaos. Combined effects of fear and harvesting are also discussed numerically.
Recommended Citation
Gupta, R. P. and Yadav, Dinesh K.
(2022).
(SI10-056) Fear Effect in a Three Species Prey-predator Food-web System With Harvesting,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 17,
Iss.
3, Article 12.
Available at:
https://digitalcommons.pvamu.edu/aam/vol17/iss3/12
Included in
Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons