Role of fear factor in a two-prey one-predator model: comparison between crisp and fuzzy environment

Abstract

A prey–predator model with fear effect on two prey species in presence of predator and the intraspecific competition between two prey species has been considered first time in crisp and fuzzy environment. To incorporate the natural imprecision present in the environmental factors, some parameters are considered as fuzzy numbers. The positivity, boundedness and the permanence of the solutions of the fuzzy system have been established here. The existence and local stability of the equilibrium points have also been discussed. In this article, we have mainly focussed on our study to examine the effect of fear on the stability of the system in crisp as well as fuzzy environment. For this reason, Hopf bifurcation analysis has been done with respect to fear factor in the crisp as well as fuzzy environment. These results are also verified numerically from computer simulation of the system.