A new 5D hyperchaotic system with stable equilibrium point, transient chaotic behaviour and its fractional-order form

Abstract

Hidden attractors with the family of stable equilibrium points in higher-dimensional systems are more interesting and difficult discover compared to other families of hidden attractors. In this paper, a new 5D hyperchaotic system is reported. The proposed system has only one stable equilibrium point. Hence, the new system belongs to the category of hidden attractors. Although some lower-dimensional chaotic systems with stable equilibrium points are available in the literature, but very few hyperchaotic systems with stable equilibrium points are reported. The new system is simple considering the number of terms, compared with the existing similar type of systems. The proposed system exhibits multistability and transient chaotic behaviour. The fractional-order counterpart of the proposed system is analysed using Adams–Bashforth–Moulton algorithm and the chaotic nature is validated by bifurcation diagram. The simulation results confirm the claims made in the paper.