Discussion on fuzzy quota harvesting model in fuzzy environment: fuzzy differential equation approach

Abstract

In the recent years much importance has been laid on the role of uncertainty (fuzzy, interval etc.) in mathematical biology. In this paper we tried to study on the quota harvesting model in fuzzy environment. This model is considered in three different ways viz. (1) Initial condition (population density) is a fuzzy number, (2) coefficients of quota harvesting model (intrinsic growth rate and quota harvesting rate) are fuzzy number and (3) both initial condition and coefficients are fuzzy number. We discuss all these fuzzy cases individually. The solution procedure is done by using the concept of fuzzy differential equation approach. We have discussed the equilibrium points and their feasibility in all the three cases. This paper explores the stability analysis of the quota harvesting model at the equilibrium points in fuzzy environment. In order to examine the stability systematically in different fuzzy cases, we have used numerical simulations and discussed them briefly.

Influence of impreciseness in designing tritrophic level complex food chain modeling in interval environment

“…Researchers have postulated many hypotheses to functionally signify the coexistence of the interacting populations in different ambiances [3][4][5][6][7][8][9][10][11][12]. Researchers have paid considerably high attention mostly on two-species or three-species predator-prey models.…”

Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

“…Nounou et al [8] illustrated glycolyticglycogenolytic pathway model, purine metabolism pathway model, and a genetic pathway using fuzzy systems strategy and developed model-free nonlinear intervention strategies. Paul et al [9] discussed the fuzzy quota harvesting of a single species Lotka-Volterra equation using generalized Hukuhara differentiability. Thus, many authors have utilized this concept for modeling in mathematical biology [10][11][12][13][14].…”

Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Fuzzy Fractional Differential Equations

“…[2]). Nowadays, the theory of fuzzy differential equations could be applicable in many areas, for instance, physics, thermodynamics, biology, medicine, chemistry and many other fields of science (see e. g., [3,4,5,6,7] and references contained therein).…”