Numerical Simulation of Nonlinear
Ecological Models with Nonlocal
and Nonsingular Fractional Derivative
Kolade M. Owolabi
1 Introduction
Over the years, the subject of ecology has been studied and becomes day-in and
day-out activities. The meaning of ecology has gone beyond monitoring a flock
of animals. In population dynamics, it has been used to address the interpersonal
relationship between two or more species, where a functional response of the higher
species (predator) to that of the lower species (prey) is known to be the change in
the density of prey attached per unit time per predator as the prey density changes.
Different types of functional response used to model various predation scenarios have
been reported in [20, 21] to compliment the realistic standard Lotka–Voltera system.
Zhang et al. [35] study the effect of periodic forcing and impulsive perturbations on
predator–prey system with Holling type-IV functional response.
In contrast to the classical single or multicomponent species dynamics that were
extensively reported in literature between the 1970s and 1980s and till date, respec-
tively [19], predator–prey systems are known to give rise to period and spatiotemporal
oscillations. Though most systems with steady-state equilibria often result to oscil-
latory transients with a stable frequency. Many (fluctuating) population scenarios
appear to be modelled by such interactions. Nonetheless, fractional predator–prey
models have been poorly reported with respect to the interaction of nonlinear dy-
namics. The total population of the mathematical model can be denoted by P, which
is subdivided into two or three groups, that is, a group referred to as the prey on
which the higher class depends for existence. The second group contains the species
K. M. Owolabi (B )
Faculty of Natural and Agricultural Sciences, Institute for Groundwater Studies,
University of the Free State, Bloemfontein 9300, South Africa
e-mail: koladematthewowolabi@tdtu.edu.vn
Faculty of Mathematics and Statistics, Ton Duc Thang University,
Ho Chi Minh City, Vietnam
© Springer Nature Singapore Pte Ltd. 2020
H. Dutta (ed.), Mathematical Modelling in Health, Social and Applied Sciences, Forum
for Interdisciplinary Mathematics, https://doi.org/10.1007/978-981-15-2286-4_10
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