Estimating the bound for the generalized Lorenz system

A chaotic system is bounded, and its trajectory is confinedto a certain region which is called the chaotic attractor. No matter howunstable the interior of the system is, the trajectory neverexceeds the chaotic attractor. In the present paper, the spherebound of the generalized Lorenz system is given, based on theLyapunov function and the Lagrange multiplier method. Furthermore, weshow the actual parameters and perform numerical simulations.