Braverman, E.Saker, S. H.2018-09-272018-09-272011-07-28E. Braverman and S. H. Saker, “On a Difference Equation with Exponentially Decreasing Nonlinearity,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 147926, 17 pages, 2011. doi:10.1155/2011/147926http://hdl.handle.net/1880/10840210.11575/PRISM/44280We establish a necessary and sufficient condition for global stabilityof the nonlinear discrete red blood cells survival model and demonstrate that local asymptoticstability implies global stability. Oscillation and solution bounds are investigated. We also showthat, for different values of the parameters, the solution exhibits some time-varying dynamics, that is,if the system is moved in a direction away from stability (by increasing the parameters), thenit undergoes a series of bifurcations that leads to increasingly long periodic cycles and finally todeterministic chaos. We also study the chaotic behavior of the model with a constant positiveperturbation and prove that, for large enough values of one of the parameters, the perturbed systemis again stable.Journal Article2018-09-27enCopyright © 2011 E. Braverman and S. H. Saker. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.https://doi.org/10.1155/2011/147926