DYNAMICAL COMPLEXITIES IN A DISCRETE-TIME PREDATOR-PREY SYSTEM AS CONSEQUENCES OF THE WEAK ALLEE EFFECT ON PREY
Citation
Kangalgil, F., Işık, S. (2023). DYNAMICAL COMPLEXITIES IN A DISCRETE-TIME PREDATOR-PREY SYSTEM AS CONSEQUENCES OF THE WEAK ALLEE EFFECT ON PREY. Miskolc Mathematical Notes, 24(1), 209-226.Abstract
In this paper, a two dimensional discrete-time predator-prey system with weak Allee
effect, affecting the prey population, is considered. The existence of the positive fixed points of
the system and topological classification of coexistence positive fixed point are examined. By
using the bifurcation theory, it is shown that the discrete-time predator-prey system with Allee effect undergoes flip and Neimark-Sacker bifurcations depending on the parameter a. The
parametric conditions for existence and direction of bifurcations are investigated. Numerical
simulations including bifurcation diagrams, phase portraits and maximum Lyapunov exponents
of the system are performed to validate analytical results. The computation of the maximum Lyapunov exponents confirm the presence of chaotic behaviour in the considered system. Finally,the
OGY feedback control method is implemented to stabilize chaos existing in the system