Abstract
Over the last decade, the chaotic behaviors of dynamical systems have been extensively explored.Recently, discovering or developing a 2D system of ordinary differential equations (ODEs) capable of exhibitingchaotic dynamical behaviors is an attractive research topic. In this study, a chaotic system with a 2D system ofnonsmooth ODEs has been developed. This system is can exhibit chaotic dynamical behaviors. Its main dynamicalbehaviors, including time-series trajectories, phase portraits of attractors, and equilibria and their stability, have beeninvestigated. The developed system has been verified by an excessive variety of fascinating chaotic behaviors, such aschaotic attractor, symmetry, sensitivity to initial conditions (ICs), fractal dimension, autocorrelation, power spectrum,Lyapunov exponent, and bifurcation diagram. Analytical and numerical simulations are used to study the dynamicalbehaviors of such a system. The developed system has extreme sensitivity to ICs, a fractal dimension of more than 1.8and less than 2.05, an autocorrelation fluctuating randomly about an average of zero, a broadband power spectrum,and one positive Lyapunov exponent. The obtained numerical simulation results have proven the capability of thedeveloped 2D system for exciting chaotic dynamical behaviors
Recommended Citation
Rahman, Zain-Aldeen S. A.; Jasim, Basil H.; and Al-Yasir, Yasir I. A.
(2022)
"Chaotic Dynamics in the 2D System of Nonsmooth OrdinaryDifferential Equations,"
Iraqi Journal for Computer Science and Mathematics: Vol. 3:
Iss.
2, Article 2.
Available at:
https://ijcsm.researchcommons.org/ijcsm/vol3/iss2/2
