Open AccessComputational dynamics of a Lotka-Volterra Model with additive Allee effect based on Atangana-Baleanu fractional derivative
Author(s) -
Hasan S. Panigoro,
Emli Rahmi
Publication year - 2021
Publication title -
jambura journal of biomathematics
Language(s) - English
Resource type - Journals
ISSN - 2723-0317
DOI - 10.34312/jjbm.v2i2.11886
Subject(s) - allee effect , fractional calculus , mathematics , hopf bifurcation , limit cycle , operator (biology) , derivative (finance) , order (exchange) , bifurcation , convergence (economics) , limit (mathematics) , mathematical analysis , statistical physics , nonlinear system , physics , population , repressor , economic growth , chemistry , sociology , financial economics , biochemistry , quantum mechanics , transcription factor , demography , finance , gene , economics
This paper studies an interaction between one prey and one predator following Lotka-Volterra model with additive Allee effect in predator. The Atangana-Baleanu fractional-order derivative is used for the operator. Since the theoretical ways to investigate the model using this operator are limited, the dynamical behaviors are identified numerically. By simulations, the influence of the order of the derivative on the dynamical behaviors is given. The numerical results show that the order of the derivative may impact the convergence rate, the occurrence of Hopf bifurcation, and the evolution of the diameter of the limit-cycle.