A hyperchaotic system from a chaotic system with one saddle and two stable node-foci (Q837138)

A new hyperchaos is generated from the system \[ \begin{cases} \dot{x} = a (y - x),\\ \dot{y} = cx - xz,\\ \dot{z} = - bz + xy,\end{cases} \] via adding a linear controller to it and its basic dynamics and properties. It is numerically verified through investigating trajectories, bifurcations path, analysis of power spectrum and Poincare projections. Finally, its ultimate boundness and two complete mathematical characterizations for the 4D Hopf bifurcation are studied.