Dynamics and Adaptive Control of a Novel 5D Hyperchaotic System: Either Hidden Attractor or Self-excited with Unusual Nature of Unstable Equilibria

In 2020, J. Sprott proposed a new three dimensional chaotic system with special features such like 1) dissipative and time-reversible; 2) no equilibrium point; 3) lien of initial conditions goes to the attractor. We observed that an extension of the so-called Sprott's 2020 system to four dimensional system with complex dynamics showed either chaotic or hyperchaotic with unbounded orbits. In this paper, a novel five dimensional hyperchaotic system based on Sprott's 2020 system has been proposed. The proposed system shows complex dynamics like hyperchaotic. The proposed system can be classified as a hidden attractor where no equilibrium point appeared or self-excited where an unusual nature of unstable equilibrium points connected to a very complicated function called Lambert W appeared. The dynamical properties of such system are discovered by computing the Lyapunov exponents and bifurcation diagram. Adaptive control to the proposed system was provided.