TITLE:
Continuous Time Dynamical System with Hidden Attractors under Mathematical Control
AUTHORS:
Maysoon M. Aziz, Abothar A. Kalalf
KEYWORDS:
Lyapunov Function, Stability, Hopf Bifurcation, Lyapunov Dimension
JOURNAL NAME:
Open Access Library Journal,
Vol.10 No.1,
January
30,
2023
ABSTRACT: In this paper, a continuous two-dimensional dynamic system is proposed. This system was analyzed by finding the equilibrium points. Also, the stability of the system was analyzed through the roots of the characteristic equation, Roth stability criteria, Hurwitz stability criteria, fractional part stability criteria, and Lyapunov function. It turns out that the system is chaotic at one point of equilibrium and stable at the other point. Also, it was found that the roots of the characteristic equation of the system were in the form of complex numbers, and the real part was relied upon in the stability analysis. And then the system was controlled using adaptive control technology.