Global dynamics and bifurcations of two second order difference equations in mathematical biology
Date of Original Version
We investigate the global behavior of two difference equations with exponential nonlinearities (forumala Presented). where the parameters b, c are positive real numbers and p ∈ (0, 1) and (forumala Presented). where the parameters a, b are positive numbers. The the initial conditions x −1 , x 0 are arbitrary nonnegative numbers. The two equations are well known mathematical models in biology which behavior was studied by other authors and resulted in partial global dynamics behavior. In this paper, we complete the results of other authors and give the global dynamics of both equations. In order to obtain our results we will prove several results on global attractivity and boundedness and unboundedness for general second order difference equations (forumala Presented). which are of interest on their own.
Journal of Computational Analysis and Applications
Kulenović, M. R.S., and Sarah Van Beaver. "Global dynamics and bifurcations of two second order difference equations in mathematical biology." Journal of Computational Analysis and Applications 28, 4 (2020): 615-627. https://digitalcommons.uri.edu/math_facpubs/143