Title

Asymptotic Approximations of the Stable and Unstable Manifolds of Fixed Points of a Two-dimensional Cubic Map

Authors

Jasmin Betešević
Mustafa Kulenovic, University of Rhode IslandFollow
Esmir Pilav

Document Type

Article

Date of Original Version

2015

Abstract

We find the asymptotic approximations of the stable and unstable manifolds of the saddle equilibrium solutions of the following difference equation x_n+1 = a x³_n + bx³_n-1 + cx_n + dx_n-1, n = 0,1... where the parameters a, b, c and d are positive numbers and the initial conditions x_-1 and x₀ are arbitrary numbers. these manifolds determine completely the global dynamics of this equation.

Citation/Publisher Attribution

Bekteševic, J., Kulenović, M. R. S., & Pilav, E. (2015). Asymptotic Approximations of the Stable and Unstable Manifolds of Fixed Points of a Two-dimensional Cubic Map. International Journal of Difference Equations, 10(1), 39-58.

Available at: http://campus.mst.edu/ijde/contents/v10n1p3.pdf