Comment on 'A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family', P. Yu, XX Liao, S.L Xie, Y.L Fu [Commun Nonlinear Sci Numer Simulat 14 (2009) 2886-2896]

摘要

In the commented paper the authors study some aspects of boundedness in the general Lorenz family, x = σ(y - x). y = px - γy -xz, z= -βz + xy, considering that it contains four independent parameters. However, as we show here by means of a linear scaling in time and coordinates, they are dealing with a system homothetically equivalent to the Lorenz system. Consequently, the novel and interesting results they provide for the general Lorenz family can be obtained working directly with the Lorenz equations, that is, dealing only with three independent parameters.