Generation of a Multiwing Hyperchaotic System With a Line Equilibrium and Its Control

Abstract This paper presents the development of a new hyperchaotic system, created by the extension of the established Lü system to the four-dimension. The complex dynamics of this new system are explored through both theoretical analysis and numerical simulations. The study focuses on the system’s dynamic behavior, equilibrium points, Lyapunov exponents, and Poincaré sections, as well as bifurcation diagrams and coexisting attractors to thoroughly characterize its properties. Moreover, two main methods were investigated to control the hyperchaos: linear feedback control and adaptive control. These approaches aim to stabilize the hyperchaotic system at unstable equilibrium points, even when system parameters are either known or unknown. Numerical simulations are performed to illustrate the effectiveness of the proposed controllers.