Bifurcation analysis and chaos control of a second-order exponential difference equation

Abstract

Abstract
The aim of this article is to study the local stability of equilibria, investigation related to the parametric conditions for transcritical bifurcation, period-doubling bifurcation and Neimark-Sacker bifurcation of the following second-order dierence equation
xn+1 =Alpha xn +Beta xn-????1 exp(Sigma ????xn-????1)
where the initial conditions x????1; x0 are the arbitrary positive real numbers and ; and Alpha, Beta and Sigma are positive constants. Moreover, chaos control method is implemented for controlling chaotic behavior under the influence of Neimark-Sacker bifurcation and period-doubling bifurcation. Numerical simulations are provided to show eeffctiveness of theoretical discussion.