A Novel 4-D Hyperchaotic Chemical Reactor System and Its Adaptive Control

Abstract

Chaos in nonlinear dynamics occurs widely in physics, chemistry, biology, ecology, secure communications, cryptosystems and many scientific branches. Chaotic systems have important applications in science and engineering. In this work, we derive a twelve-term novel 4-D hyperchaotic system by introducing a state feedback control to the 3-D chemical chaotic reactor obtained by Huang, Yang, J Math Chem 38(1):107–117, 2015, [11]. The phase portraits of the twelve-term novel hyperchaotic chemical reactor system are depicted and the qualitative properties of the novel hyperchaotic system are discussed. The Lyapunov exponents of the novel hyperchaotic chemical reactor system are obtained as \(L_1 = 0.2263\), \(L_2 = 0.0365\), \(L_3 = 0\) and \(L_4 = -10.8396\). Also, the Kaplan–Yorke dimension of the novel hyperchaotic chemical reactor system is obtained as \(D_{KY} = 3.0240\). Since the sum of the Lyapunov exponents is negative, the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to globally stabilize the novel hyperchaotic system with unknown parameters. Finally, an adaptive controller is also designed to achieve global chaos synchronization of the identical hyperchaotic systems with unknown parameters. MATLAB simulations are depicted to illustrate all the main results derived in this work.