Hidden extreme multistability in a novel 4D fractional-order chaotic system

The hidden attractor and extreme multistability are very important topics in nonlinear dynamics. In this paper, by adding a further variable in a three-dimensional chaotic system, a novel four-dimensional fractional-order chaotic system is developed. This system consists of eight terms including three different nonlinear terms and one constant term. What interests us is that this newly presented system has no-equilibrium but it can also exhibit rich and complex hidden dynamics. Furthermore, the offset boosting of a variable of the proposed chaotic system can be achieved by adjusting the constant term. The intricate hidden dynamic properties of the proposed chaotic system are investigated by employing conventional nonlinear dynamical analysis tools including equilibrium, phase planes, bifurcation diagrams and Lyapunov exponents, chaos diagrams, etc. Finally, Multisim simulations and the corresponding hardware experiments are implemented to validate the theoretical analysis.