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Basin boundaries with nested structure in a shallow arch oscillator

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Abstract

The basin boundaries with nested structure are investigated in a shallow arch oscillator. Basin organization is complex yet systematic and it is governed by the ordering of heteroclinic and homoclinic connections of regular saddles. The Wada properties are verified for eight basin boundaries, where five basin boundaries are totally Wada basin boundaries for a given set of parameters. The organization of nested basin boundaries is governed by the order of saddle connections. The term “Wada number” is introduced to describe the nested structure. The partially Wada basin boundaries are investigated by the erodent cells and the remnant cells.

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Acknowledgments

The authors are deeply indebted to the 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 paper. This work was supported by the National Natural Science Foundation of China (No. 11002092).

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Authors and Affiliations

  1. College of Science, Shenyang Agricultural University, Shenyang, 110866, China

    Yongxiang Zhang

  2. Department of Mathematics, Tianjin University, Tianjin , 300072, China

    Liang Fu Lu

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  1. Yongxiang Zhang
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  2. Liang Fu Lu
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Correspondence to Yongxiang Zhang or Liang Fu Lu.

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Zhang, Y., Lu, L.F. Basin boundaries with nested structure in a shallow arch oscillator. Nonlinear Dyn 77, 1121–1132 (2014). https://doi.org/10.1007/s11071-014-1364-7

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