THEORETICAL AND NUMERICAL ANALYSIS OF PIECEWISE LOTKA–VOLTERRA PREY–PREDATOR MODELS WITH STOCHASTIC DIFFERENTIAL OPERATORS

Abstract

This paper proposes a collection of nonlinear differential operators. The goal of the work is to develop certain theoretical and analytical intuitions regarding the replacement of the general deferential operators with the derivatives of Caputo, Atangana–Baleanu, and Caputo–Fabrizio. A variety of well-known methodologies were used to examine the models. The Lagrange interpolation polynomial was used to establish a numerical method to solve the models under investigations. We have investigated the related perspective on existence and uniqueness through this work. Several numerical findings were incorporated. The updated models examine the impact of competition on prey and predator abundance. A species’ variations in abundance are modeled as a function of the abundance of its competitors; the specific competitive mechanism is neither investigated nor stated in explicit terms.