Discontinuity, Nonlinearity, and Complexity
Global Stability Analysis of a General Scalar Difference Equation
Discontinuity, Nonlinearity, and Complexity 7(3) (2018) 225232  DOI:10.5890/DNC.2018.09.001
Huseyin Merdan$^{1}$, Ozlem Ak Gumus$^{2}$, Gamzegul Karahisarli$^{1}$
$^{1}$ Department of Mathematics, TOBB University of Economics and Technology, Ankara, Turkey
$^{2}$ Department of Mathematics, Adiyaman University, Adiyaman, Turkey
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Abstract
We consider a general firstorder scalar difference equation with and without Allee effect. The model without Allee effect represents asexual reproduction of a species while the model including Allee effect represents sexual reproduction. We analyze global stabilities of both models analytically and compare the results obtained. Numerical simulations are included to support the analytical results. We conclude that Allee effect has a destabilizing effect on the global stability of the model. This result is different from the local stability behaviour of the same fixed point of the model.
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