Quantifying stability and chaoticity of one-dimensional and two-dimensional discrete dynamical systems using stability analysis and lyapunov exponents / Ummu Atiqah Mohd Roslan and Ng Wee Chee

Mohd Roslan, Ummu Atiqah and Chee, Ng Wee (2020) Quantifying stability and chaoticity of one-dimensional and two-dimensional discrete dynamical systems using stability analysis and lyapunov exponents / Ummu Atiqah Mohd Roslan and Ng Wee Chee. Mathematical Sciences and Informatics Journal (MIJ), 1 (1). pp. 1-9. ISSN 2735-0703

Abstract

Discrete dynamical system is a system that evolve dynamically with discrete time. In this paper, we consider two discrete systems which exhibit chaotic behaviour. We show that the chaoticity of a system is depend on the values of parameter in the system. The objective of this paper is to investigate both stability and chaoticity of the systems using stability analysis and Lyapunov exponent, respectively. The results show that there is only one fixed point for the one-dimensional system, while for the two-dimensional system, there exist four possible fixed points. We have proved the stability conditions for each fixed point obtained. The Lyapunov results show that the one-dimensional system is stable when r<n/2 and chaotic when r>n/2. Whereas for two-dimensional systems considered, the system is chaotic for the whole range of parameter aE(0,1]. This study shows that it is significant to consider various values of parameter to study the stability of a dynamical systems in particular to control the chaos in a system.

Metadata

Item Type: Article
Creators:
Creators
Email / ID Num.
Mohd Roslan, Ummu Atiqah
ummuatiqah@umt.edu.my
Chee, Ng Wee
s42719@student.umt.edu.my
Subjects: Q Science > QA Mathematics > Analysis
Divisions: Universiti Teknologi MARA, Perak > Tapah Campus > Faculty of Computer and Mathematical Sciences
Journal or Publication Title: Mathematical Sciences and Informatics Journal (MIJ)
UiTM Journal Collections: UiTM Journal > Mathematical Science and Information Journal (MIJ)
ISSN: 2735-0703
Volume: 1
Number: 1
Page Range: pp. 1-9
Keywords: Stability; Fixed point; Lyapunov exponent; Discrete dynamical system
Date: August 2020
URI: https://ir.uitm.edu.my/id/eprint/61807
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