In this paper, it is proved that the period-doubling bifurcation of the solutions of the first order exponential Logistic iterative equation is existent. The equation that must be satisfied by critical bifurcation parameters is given. And it is showed that the critical bifurcation parameter sequence has a limit. Then, it is proved that the first order exponential Logistic iterative equation has a chaotic solution when the parameter is over the limit.
Hui Jing CAI.
On the Period-Doubling Bifurcation of the Solutions of the First Order Exponential Logistic Iterative Equation. Acta Mathematica Sinica, Chinese Series, 2001, 44(4): 761-768 https://doi.org/10.12386/A2001sxxb0098