Modified Lotka Volterra Model with Perspectives of the Piecewise Derivative

TL;DR

This paper extends the Lotka-Volterra predator-prey model by incorporating piecewise derivatives and numerical solutions, revealing piecewise patterns in real-world biological interactions.

Contribution

It introduces a novel approach using piecewise derivatives and the Adams-Bashforth method to analyze predator-prey dynamics.

Findings

Piecewise patterns observed in predator-prey behaviors

Numerical solutions demonstrate model's real-world applicability

Enhanced understanding of species interactions

Abstract

This study uses the Lotka Volterra Predator-Prey model to offer a notion of piecewise patterns for the various piecewise derivatives. Using the piecewise derivatives, we produced numerical solutions that are referred to as the Adams-Bashforth method. The computer results show piecewise patterns in the Lotka Volterra Predator-Prey model's real-world behaviours. The Lotka-Volterra model looks into the relationships between competition and abundance between two competing species. Changes in the abundance of one species are modelled as a function of the abundance of its competitors, but the competitive mechanism is given and evaluated. This notion led some scholars to label certain mathematical expressions as "phenomenological" and to propose a different theoretical framework that gives resources special consideration. The Lotka-Volterra model, often called the predator-prey model or the Lotka-Volterra model, is a nonlinear mathematical expression that is frequently used to analyse the dynamical behaviours of biological systems in which two species interact, one as a predator and the other as prey. The variation in the populations over time is illustrated by the mathematical statement.