Dynamics and simulations of discretized Caputo-conformable fractional-order Lotka–Volterra models

Abstract

In this article, a prey–predator system is considered in Caputo-conformable fractional-order derivatives. First, a discretization process, making use of the piecewise-constant approximation, is performed to secure discrete-time versions of the two fractional-order systems. Local dynamic behaviors of the two discretized fractional-order systems are investigated. Numerical simulations are executed to assert the outcome of the current work. Finally, a discussion is conducted to compare the impacts of the Caputo and conformable fractional derivatives on the discretized model.

Keywords

• caputo fractional derivative
• conformable fractional derivative
• prey–predator system
• discretization
• stability
• bifurcations
• chaos