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June  2017, 22(4): 1673-1681. doi: 10.3934/dcdsb.2017080

## On global boundedness of the Chen system

 1 College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China 2 Mathematical post-doctoral station, College of Mathematics and Statistics, Southwest University, Chongqing 400716, China 3 College of Electronic and Information Engineering, Southwest University, Chongqing 400716, China 4 College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China 5 College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Received  June 2016 Revised  September 2016 Published  February 2017

This paper deals with the open problem of the global boundedness of the Chen system based on Lyapunov stability theory, which was proposed by Qin and Chen (2007). The innovation of the paper is that this paper not only proves the Chen system is global bounded for a certain range of the parameters according to stability theory of dynamical systems but also gives a family of mathematical expressions of global exponential attractive sets for the Chen system with respect to the parameters of this system. Furthermore, the exponential rate of the trajectories is also obtained.

Citation: Fuchen Zhang, Xiaofeng Liao, Chunlai Mu, Guangyun Zhang, Yi-An Chen. On global boundedness of the Chen system. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1673-1681. doi: 10.3934/dcdsb.2017080
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