Fractional calculus in ecological systems: Bifurcation analysis and continuation techniques for discrete Lotka–Volterra models

Abstract

This study explores the application of fractional calculus to discrete Lotka–Volterra models, which are fundamental in ecological systems. By incorporating fractional differentiation, we capture the memory effects and long‐range dependencies that are characteristic of real‐world ecological dynamics. Our analysis employs bifurcation analysis and continuation methods to investigate the intricate dynamics that emerge in these systems. We find that the fractional order of differentiation significantly impacts the stability and oscillatory behavior of the ecological system, providing novel insights into the dynamics of predator–prey interactions. Our results demonstrate the enhanced accuracy and applicability of fractional‐order models in ecological modeling, highlighting their potential for more realistic simulations of complex ecological systems.