The orbital stability of the trajectories of dynamic systems (Q1185616)

The system \(\dot x=f(x)\), \(x\in R^ n\) is considered, where \(f(x)\) is a twice continuously differentiable vector-valued function. An orbital stability criterion, generalizing the method of Lyapunov function, is given. The global asymptotical stability of the Lorenz system \(\dot x=- d(x-y)\), \(\dot y=rx-y-xz\), \(\dot z=-bz+xy\), \(d>0\), \(r>1\), \(b>0\), is also considered by the author.