A note on “Introduction and synchronization of a five-term chaotic system with an absolute-value term-in [Nonlinear Dyn. 73 (2013) 311-23] by Pyung Hun Chang and Dongwon Kim

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• 作者：Haijun Wang ; Xianyi Li
• 关键词：Chaotic system ; Heteroclinic orbit ; Numerical simulation ; 34C23 ; 34C37 ; 34D08 ; 34D20
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：81
• 期：1-2
• 页码：1017-1019
• 全文大小：980 KB
• 参考文献：1.Chang, P., Kim, D.: Introduction and synchronization of a five-term chaotic system with an absolute-value term. Nonlinear Dyn. 73(1-), 311-23 (2013)MATH MathSciNet View Article
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  13.Liu, Y., Pang, W.: Dynamics of the general Lorenz family. Nonlinear Dyn. 67(2), 1595-611 (2012)MATH MathSciNet View Article
  14.Li, X., Wang, P.: Hopf bifurcation and heteroclinic orbit in a 3D autonomous chaotic system. Nonlinear Dyn. 73(1-), 621-32 (2013)MATH
  15.Chen, Y., Yang, Q.: Dynamics of a hyperchaotic Lorenz-type system. Nonlinear Dyn. 77(3), 569-81 (2014)View Article
  16.Wang, H., Li, X.: More dynamical properties revealed from a 3D Lorenz-like system. Int. J. Bifurc. Chaos 24(10), 29 (2014). doi:10.-142/?S021812741450133-
  
• 作者单位：Haijun Wang (1)
  Xianyi Li (1)
  
  1. College of Mathematical Science, Yangzhou University, Yangzhou, 225002, People’s Republic of China
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

In the paper entitled “Introduction and synchronization of a five-term chaotic system with an absolute-value term-in [Nonlinear Dyn. 73 (2013) 311-23], Pyung Hun Chang and Dongwon Kim proposed the following 3D chaotic system \(\dot{x}= a(y - x),\, \dot{y}= xz,\, \dot{z}= b|y| - y^{2}\). Combining theoretical analysis with numerical technique, they studied its dynamics, including the equilibria and their stability, Lyapunov exponents, Kaplan–Yorke dimension, frequency spectrum, Poincaré maps, bifurcation diagrams and synchronization. In particular, the authors formulated a conclusion that the system has two and only two heteroclinic orbits to \(S_{0}=(0, 0, 0)\) and \(S_{\pm }=(\pm b, \pm b, 0)\) when \(b\ge 2a >0\). However, by means of detailed analysis and numerical simulations, we show that both the conclusion itself and the derivation of its proof are erroneous. Furthermore, the conclusion contradicts Lemma 3.2 in the commented paper. Therefore, the conclusion in that paper is wrong.