Asymptotic approximations of a stable and unstable manifolds of a two-dimensional quadratic map

Authors

J. Bektešević, University of Sarajevo
M. R.S. Kulenović, University of Rhode Island
E. Pilav, University of Sarajevo

Document Type

Article

Date of Original Version

1-1-2016

Abstract

We find the asymptotic approximations of the stable and unstable manifolds of the saddle equilibrium solutions and the saddle period-two solutions of the following difference equation xn+1= cx2n-1+dxn+1; where the parameters c and d are positive numbers and initial conditions x-1and x0are arbitrary nonnegative numbers. These manifolds determine completely global dynamics of this equation.

Publication Title, e.g., Journal

Journal of Computational Analysis and Applications

Volume

21

Issue

1

Citation/Publisher Attribution

Bektešević, J., M. R. Kulenović, and E. Pilav. "Asymptotic approximations of a stable and unstable manifolds of a two-dimensional quadratic map." Journal of Computational Analysis and Applications 21, 1 (2016): 35-51. https://digitalcommons.uri.edu/math_facpubs/161