Open AccessEffect of fear on two predator-one prey model in deterministic and fluctuating environment
Author(s) -
Debasis Mukherjee
Publication year - 2021
Publication title -
mathematics in applied sciences and engineering
Language(s) - English
Resource type - Journals
ISSN - 2563-1926
DOI - 10.5206/mase/13541
Subject(s) - predation , predator , uniqueness , stability (learning theory) , hopf bifurcation , equilibrium point , ecology , mathematics , biology , control theory (sociology) , bifurcation , computer science , physics , mathematical analysis , nonlinear system , artificial intelligence , quantum mechanics , machine learning , differential equation , control (management)
Recent ecological studies on predator-prey interactions has concentrated on determining the impacts of antipredator behavior due to fear of predators. These studies are mainly confined into one predator-one prey system. But in case of multiple predator attack on single prey species, fear mechanism is still unknown. The combined impact of multiple predator often cannot be anticipated from their independent effects. So coexistence of multiple predators and prey’s fitness becomes an important issue from an ecological point of view. Based on the above observations, we proposed and analyzed a model consisting of two competing predator sharing a common prey where prey’s reproduction rate is affected due to fear generated by the predators. We first study the boundedness, uniform persistence, stability and Hopf bifurcation of the deterministic model. Thereafter, we have investigated the existence and uniqueness of the global positive solution, boundedness, asymptotic stability of the stochastic model. Numerical examples are provided to support our obtained results.