A normalized time-fractional Lotka--Volterra model

Abstract

In this study, we present a normalized time-fractional Lotka--Volterra model by using a normalized time-fractional derivative. To reflect memory property in biological systems, the time-fractional Lotka--Volterra model extends the traditional Lotka--Volterra system, which models predator-prey dynamics, by incorporating fractional calculus. The normalized fractional derivative possesses distinct advantages over existing fractional derivatives, notably the property that the sum of the weighting function equals 1. We provide a comprehensive description for a numerical solution algorithm of the proposed model and conduct computational simulations to illustrate the effects of varying the fractional order on predator-prey interactions. This study contributes to the ongoing development of fractional-order models in population dynamics and provides new insights into the behavior of predator-prey systems governed by fractional time evolution.