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Global attractive sets of a novel bounded chaotic system

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Abstract

This paper is concerned with the boundedness of solutions of a new chaotic system. For this system, the global exponential attractive set and positively invariant set are derived based on generalized Lyapunov function theory and the extremum principle of function. Furthermore, we can conclude that the rate of the trajectories of the system going from the exterior of the attractive set Φ λ to the interior of the attractive set Φ λ is an exponential rate. The rate of the trajectories is also obtained. Numerical simulations are presented to show the effectiveness of the proposed scheme.

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Acknowledgments

This research was supported by the Talents Project of Sichuan University of Science and Engineering (No. 2011RC07), the Key Project of Artificial Intelligence Key Laboratory of Sichuan Province (No. 2011RZJ02), the Science and Technology Key Project of Zigong (No. 2012D09), the Cultivation Project of Sichuan University of Science and Engineering (No. 2012PY19), the National Natural Science Foundation of China (Grant No: 11301570), the Basic and Advanced Research Project of CQCSTC (Grant No: cstc2013jcyjA00003), the China Postdoctoral Science Foundation funded project (Grant No: 2013M540697) and the Research Fund of Chongqing Technology and Business University (Grant No: 2013-56-03). The authors are grateful to thank the anonymous referees and editors for their valuable comments and suggestions. Without their constructive comments, the paper would not be at current quality.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, People’s Republic of China

    Fuchen Zhang & Xiang-Kai Sun

  2. School of Foreign Languages, Southwest Petroleum University, Chengdu, 610500, People’s Republic of China

    Guangyun Zhang

  3. School of Automatic and Electronic Information, Sichuan University of Science and Engineering, Zigong, 643000, People’s Republic of China

    Da Lin

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  1. Fuchen Zhang
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  2. Guangyun Zhang
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  3. Da Lin
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  4. Xiang-Kai Sun
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Correspondence to Fuchen Zhang.

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Zhang, F., Zhang, G., Lin, D. et al. Global attractive sets of a novel bounded chaotic system. Neural Comput & Applic 25, 1177–1183 (2014). https://doi.org/10.1007/s00521-014-1601-5

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  • DOI: https://doi.org/10.1007/s00521-014-1601-5

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