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Further Results on Ultimate Bound on the Trajectories of the Lorenz System

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Abstract

This paper gives further results on ultimate bound on the trajectories of the Lorenz system based on Lyapunov function stability theory. Explicit estimations of the ultimate bounds are derived. The meaningful contribution of this article is that the results presented in this paper contain the existing results as special cases. Computer simulation results show that the proposed method is effective.

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Acknowledgments

This research is supported by the National Natural Science Foundation of China (Grant No: 11426047), the Basic and Advanced Research Project of CQCSTC (Grant No: cstc2014jcyjA00040) and the Research Fund of Chongqing Technology and Business University (Grant No: 2014-56-11). The authors wish to thank the editors and reviewers for their conscientious reading of this paper and their numerous comments for improvement which were extremely useful and helpful in modifying the paper.

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Correspondence to Fuchen Zhang.

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Zhang, F., Zhang, G. Further Results on Ultimate Bound on the Trajectories of the Lorenz System. Qual. Theory Dyn. Syst. 15, 221–235 (2016). https://doi.org/10.1007/s12346-015-0137-0

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