Stability analysis of fuzzy differential equation for prey-predator system under Z-number fuzzy and granular differentiability concept

The stability analysis is one of the basic problems in the field of system, prey-predator, production inventory control, signal processing etc. The goal of stability analysis for prey-predator and production inventory control model is to determine the region of the different variables and parameters at which the system is stable or unstable. This paper explores an uncertain prey-predator model where both prey and predator populations are fuzzy variables. Also we have considered all the prey-predator parameters of the system are imprecise. This fuzzy prey-predator model is converted to an equivalent crisp model using granular differentiability approach. The condition of local stability is obtained mathematically by analysis the eigenvalues of characteristic equation. And also we introduced a production inventory model as a case study of fuzzy dynamical system to illustrate the efficiency of the result and practical aspects.