Dynamic Analysis and Synchronization of a New Chaotic System with a Circle Equilibrium and Two Perpendicular Lines of Equilibrium Points

Aceng Sambas, Sukono, Sundarapandian Vaidyanathan, Yuyun Hidayat, SenZhang, Gugun Gundara, MohamadAfendee Mohamed

This work reports a new three-dimensional chaotic system with circle equilibrium and two perpendicular lines of equilibrium points on the (x, y) plane. A detailed dynamic analysis has been performed on the new chaotic system with the help of bifurcation diagram, Lyapunov exponents spectrum, etc. It is shown that the new chaotic system is dissipative. Since the new chaotic system has infinitely many equilibriumpoints, it exhibits hidden attractor. It is also interesting to note that the new chaotic system shows multistability and it is verified bydemonstrating that there are coexisting attractors for the new chaotic system for different initial conditions. Using adaptive control, globalchaos synchronization of the new chaotic system with itself is proved using Lyapunov stability theory.

Volume 12 | Issue 2

Pages: 573-584

DOI: 10.5373/JARDCS/V12I2/S20201079