On a parametrized difference equation connecting chaotic and integrable mappings

2021/07/17 by Tomoko Nagai, Nagai, Tomoko, Atsushi Nagai +5
Mathematics · Medicine · Physics and Astronomy · #65P20 #Advanced Differential Equations and Dynamical Systems #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #G.0 #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2107.08224

openalex publication_date 2021/07/17 · openalex created_date 2021/08/02 · openalex updated_date 2026/07/28

Abstract

We present a new difference equation with two parameters c in [0,1] and A in [1,4]. This equation is equivalent to the logistic mapping if c=1 and the Morishita mapping if c=0, which are the well-known chaotic and integrable mappings, respectively. We first consider the case A=4 and investigate the time evolution by changing the parameter c in [0,1]. We next change both two parameters A in [3,4] and c in [0,1] and present the corresponding 3D bifurcation diagram.

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