Stability, Chaos Diagnose and Adaptive Control of Two Dimensional Discrete - Time Dynamical System

Autor:	Omar M. Jihad, Maysoon M. Aziz
Rok vydání:	2021
Předmět:	Nonlinear Sciences::Chaotic Dynamics Lyapunov function symbols.namesake Adaptive control Discrete time and continuous time Phase space symbols Applied mathematics Lyapunov exponent Fixed point Dynamical system Bifurcation Mathematics
Zdroj:	OALib. :1-13
ISSN:	2333-9705 2333-9721
DOI:	10.4236/oalib.1107270
Popis:	In this paper 2D discrete time dynamical system is presented. The fixed points were found. The stability of fixed points is measured by characteristic roots, jury criteria, Lyapunov function. All show that the system is unstable, and analyzing the dynamic behavior of the system finds bifurcation diagrams at the bifurcation parameter. Newton’s Raphson numerical method was used the roots of the system with the minimum error. Then, chaoticity is measured by the phase space; maximum Lyapunov exponent is obtain as (Lmax=2.394569); Lyapunov dimension is obtain as (DL=3.366413); binary test (0 - 1) is obtain as (k = 0.982). All show that the system is chaotic. Finally, the adaptive control was performed. Moreover, theoretical and graphical results of the system after control show the system is stable and Lyapunov exponent is obtained as: L1=-0.390000, L2=-0.500000, so the system is regular.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::68c9e6d504242b79aca6bfe1f57aa84b https://doi.org/10.4236/oalib.1107270 Zobrazit plný text záznamu