Abstract
Based on the method of Poincaré mapping under cell reference, we describe basins of attraction for coexisting multi-dimensional tori attractors in a three-degree-of-freedom vibro-impact system. Because the multi-dimensional tori attractors are very rare in the low-dimensional systems, we find that these coexisting tori attractors have positive measure basins in the sense of Milnor. The coexisting multi-dimensional tori attractors can be distinguished by the exactly Poincaré mapping and Lyapunov dimension. The basin of attraction can be estimated by the limit cycle in the Poincaré section from the viewpoint of engineering.
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Acknowledgments
The authors are deeply indebted to all anonymous reviewers for their careful reading of the manuscript, as well as for their fruitful comments and advice which led to an improvement of this Letter. We would like to thank you very much for helping us to correct some minor points in the manuscript. This work was supported by the National Natural Science Foundation of China (Nos. 61034005 and 61433004) and the National High Technology Research and Development Program of China (2012AA040104) and IAPI Fundamental Research Funds 2013ZCX14. This work was supported also by the development project of key laboratory of Liaoning province and supported by the NSFC (Nos. 11172119 and 11362008).
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Zhang, H., Zhang, Y. & Luo, G. Basins of coexisting multi-dimensional tori in a vibro-impact system. Nonlinear Dyn 79, 2177–2185 (2015). https://doi.org/10.1007/s11071-014-1803-5
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DOI: https://doi.org/10.1007/s11071-014-1803-5