Comment on ¡°A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family¡±, P. Yu, X.X. Liao, S.L. Xie, Y.L. Fu [Commun Nonlinear Sci Numer Simulat 14 (2009) 2886-2896]
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- 作者：Antonio Algaba ; Fern ; o Fern¨¢ndez-S¨¢nchez ; Manuel Merino ; Alej ; ro J. Rodr¨ªguez-Luis
- 关键词：General Lorenz family ; Globally exponentially attractive set ; Positive invariant set ; Generalized Lyapunov function ; Ultimate boundness of chaotic system
- 刊名：Communications in Nonlinear Science and Numerical Simulation
- 出版年：2014
- 出版时间：March, 2014
- 年：2014
- 卷：19
- 期：3
- 页码：758-761
- 全文大小：2512 K
文摘
In the commented paper the authors study some aspects of boundedness in the general Lorenz family, , 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.