Nonautonomous Riccati difference equation with real k-periodic (k≥ 1) coefficients

2016/09/05 by Azizi Raouf, Azizi, Raouf
Mathematics · Medicine · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1610.01499

openalex publication_date 2016/09/05 · openalex created_date 2016/10/14 · openalex updated_date 2026/07/28

Abstract

We study the non-autonomous Riccati difference equation x_n+1=(a_nx_n+b_n)/(c_nx_n+d_n), n=0,1,2,⋯ where (a_n)_n≥0, (b_n)_n≥0, (c_n)_n≥0, and (d_n)_n≥0 are k-periodic sequences, k≥ 1, with initial value x₀ ∈ ℝ. Precisely we give a detailed analysis of the forbidden set and the character of the solutions.

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