Bifurcation Analysis and Chaos Control of a Second-Order Exponential Difference Equation

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 difference equation x(n+1) = alpha x(n) + beta x(n-1) exp(-sigma x(n-1)) where the initial conditions x(-1), x(0) are the arbitrary positive real numbers 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 effectiveness of theoretical discussion.