Qualitative study and adaptive control of a novel 4-D hyperchaotic system with three quadratic nonlinearities

Abstract

In this work, we announce an eleven-term novel 4-D hyperchaotic system with three quadratic nonlinearities. The phase portraits of the eleven-term novel hyperchaotic system are depicted and the qualitative properties of the novel hyperchaotic system are discussed. The novel hyperchaotic system has a unique equilibrium at the origin, which is a saddle point. The Lyapunov exponents of the novel hyperchaotic system are obtained as L1 = 2.0836, L2 = 0.1707, L3 = 0 and L4 = −26.6499. The maximal Lyapunov exponent of the novel hyperchaotic system is found as L1 = 2.0836. Also, the Kaplan-Yorke dimension of the novel hyperchaotic system is derived as DKY = 3.0846. 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.