On the asymptotic stability of a rational multi-parameter first order difference equation

2010/11/15 by M. Shojaei, Shojaei, M.
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1011.3503

Submitted to Nonlinear Analysis:Real World Applications

arxiv created 2010/11/16 · arxiv updated 2010/11/17

Abstract

In this part we study the dynamics of the following rational multi-parameter first order difference equation x_n+1 =(ax_n³+ bx_n²+cx_n + d)/x_n³, x₀∈ R⁺ where the parameters a, b, d together with the initial condition x₀ are positive while the parameter c could accept some negative values. We investigate the equilibria and 2-cycles of this equation and analyze qualitative and asymptotic behavior of it's solutions such as convergence to an equilibrium or to a 2-cycle.

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