Abstract
In this work, we describe a seven-term two-scroll novel chaotic system with three quadratic nonlinearities. The phase portraits of the two-scroll novel chaotic system are illustrated and the dynamic properties of the novel chaotic system are discussed. The novel chaotic system has two unstable equilibrium points. We show that the equilibrium point at the origin is a saddle point, while the other equilibrium point is a saddle-focus. The novel chaotic system has rotation symmetry about the \(x_3\) axis. The Lyapunov exponents of the novel chaotic system are obtained as \(L_1 = 3.1464\), \(L_2 = 0\) and \(L_3 = -24.0635\), while the Kaplan–Yorke dimension of the novel chaotic system is obtained as \(D_{KY} = 2.1308\). Since the sum of the Lyapunov exponents is negative, the novel chaotic system is dissipative. Next, we derive new results for the global chaos control of the novel two-scroll chaotic system with unknown parameters using adaptive control method. We also derive new results for the global chaos synchronization of the identical novel two-scroll chaotic systems using adaptive control method. The main control results are established using Lyapunov stability theory. MATLAB simulations are shown to illustrate the phase portraits of the novel two-scroll chaotic system and also the adaptive control results derived in this work.
Published Version
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