TITLE:
Nonlinear 6D Dynamical System with Hidden Attractors and Its Electronic Circuit
AUTHORS:
Maysoon M. Aziz, Abothar A. Kalalf
KEYWORDS:
Lyapunov Function, Stability, Hopf Bifurcation, Lyapunov Dimension, Electronic Circuit
JOURNAL NAME:
Open Access Library Journal,
Vol.10 No.1,
January
30,
2023
ABSTRACT: In this paper, a six-dimensional model of continuous time dynamical systems is proposed. This system was analyzed by finding equilibrium points, and the stability of the system was also analyzed using different methods, namely the roots of the characteristic equation, Routh’s invariance criterion, Hurwitz’s invariance criterion, Lyapunov function, and the continued fraction stability criterion. The chaoticity of the system was tested by Lyapunov exponent, the hexagonal system was found to be chaotic. The dissipation and Hopf Bifurcation of the proposed system were also found, and then the system was controlled using the adaptive control technique. Finally, the results and numerical figures before and after control were compared for the system under study. An electronic circuit was created as a six-dimensional system application consisting of twelve resistors, six capacitors, six voltages and six operational amplifiers, where the results were obtained from Multisim12, and it was found that the designed electronic circuit simulates the theoretical results of the six-dimensional dynamical system well.