On p-adic cubic generalized logistic dynamical system

• Main Authors: Mukhamedov, Farrukh, Wan Rozali, Wan Nur Fairuz Alwani
• Format: Conference or Workshop Item
• Language: English; English
• Published: IOP Publishing Ltd 2013
• Subjects: QA Mathematics; QA300 Analysis; QC Physics
• Online Access: http://irep.iium.edu.my/72746/1/Mukhamedov_2013_J._Phys.__Conf._Ser._435_012012.pdf; http://irep.iium.edu.my/72746/7/72746%20On%20a%20p-adic%20cubic%20generalized%20logistic%20dynamical%20system%20SCOPUS.pdf; http://irep.iium.edu.my/72746/; https://iopscience.iop.org/article/10.1088/1742-6596/435/1/012012/pdf

Applications of p-adic numbers mathematical physics, quantum mechanics stimulated increasing interest in the study of p-adic dynamical system. One of the interesting investigations is p-adic logistics map. In this paper, we consider a new generalization, namely we study a dynamical system of the form fa(x) = ax(1−x2). The paper is devoted to the investigation of a trajectory of the given system. We investigate the generalized logistic dynamical system with respect to parameter a and we restrict ourselves for the investigation of the case |a|p < 1. We study the existence of the fixed points and their behavior. Moreover,wedescribetheirsizeofattractorsandSiegeldiscssincethestructureoftheorbitsofthesystem is related to the geometry of the p-adic Siegel discs.