Analysis and simulation of herd behaviour dynamics based on derivative with nonlocal and nonsingular kernel

Abstract

A two-component system modelling the interaction between a prey and predator which cohabit together in nonlinear fashion in a given habitat is considered in this paper using the concept of fractional derivative. In the herb dynamical system, the classical time-derivative is modeled with the Atangana-Baleanu fractional-order operator which combines both nonlocal and nonsingular kernels in its formulation. A recent numerical scheme based on the Adams-Bashforth method is applied to approximate the fractional derivatives. To ensure the correct choice of parameters that are biologically meaningful in such dynamics, we examine the model for stability analysis. Numerical results are given for different parameter values of γ∈(0<γ⩽1] to justify our theoretical findings.