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Basin reversal in nonlinear driven oscillators

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Abstract

A new type of basin catastrophe is investigated in two-dimensional driven oscillators. We identify the organization of multiple coexisting basins of attraction before and after the basin catastrophe. Before the catastrophe, all basins spiral outward toward the attractor at infinity in reverse iteration. After the catastrophe, the systematic basin organization is interrupted and some basins spiral inward toward the unstable attractors. This type of basin catastrophe is called basin reversal. The underlying mechanism for basin reversal is discovered by the reversible manifold of the regular saddles. We further analyze that the origin of the emerging abrupt reversal is related to a limit cycle.

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Acknowledgements

The authors are deeply indebted to all anonymous reviewers and the editor 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. 11572205 and No. 11732014).

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Authors and Affiliations

  1. University of Jinan Library, University of Jinan, Jinan, 250022, Shandong, China

    Guiqin Kong

  2. School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, China

    Yongxiang Zhang

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  1. Guiqin Kong
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Kong, G., Zhang, Y. Basin reversal in nonlinear driven oscillators. Nonlinear Dyn 96, 1213–1231 (2019). https://doi.org/10.1007/s11071-019-04849-2

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