Stability and Period-Doubling Bifurcation in a Modified Commensal Symbiosis Model with Allee Effect

Authors : Seval IŞIK

Pages : 310-324

Doi:10.18185/erzifbed.879963

View : 28 | Download : 9

Publication Date : 2022-03-27

Article Type : Research Paper

Abstract :In this article, the qualitative behaviour of discrete-time commensal symbiosis model which is obtained by implementing the forward Euler’s scheme is discussed in detail. Firstly, the local stability conditions of fixed points of the model are studied. It is proved that the considered model undergoes Period-Doubling bifurcation around coexistence fixed point with the help of bifurcation theory. In order to support the accuracy of obtained analytical finding, some parameter values have been determined and numerical simulations are carried out for these parameter values. Numerical simulations display new and rich nonlinear dynamical behaviours. More specifically, when the parameter
Keywords : Allee effect, stability, Period Doubling bifurcation