A no-equilibrium hyperchaotic system with a cubic nonlinear term

Discovering dynamical systems with hidden attractors has become an attractive topic recently. A novel four-dimensional continuous-time autonomous system with a cubic nonlinear term is introduced in this work. It is worth noting that this no-equilibrium system can generate hidden hyperchaotic attractors. The fundamental properties of such systems are investigated by means of equilibrium points, phase portrait, bifurcation diagram and Lyapunov exponents. In addition, an adaptive scheme has been presented to synchronize two such identical hyperchaotic systems. Moreover, an electronic circuit is also designed and implemented to verify the feasibility of the theoretical model.