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Switching-induced Wada basin boundaries in the Hénon map

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Abstract

Whether Wada basin boundaries can occur typically in dynamical systems other than smooth systems has been an open question. We verify the existence of Wada basin boundaries in a switched Hénon map. We combine two basin boundaries (non-Wada property) but when they are alternated in periodic manners the Wada basin boundaries can be created. We give some mathematically rigorous results guaranteeing these emerging Wada basin boundaries by the auxiliary dynamics method. It suggests that switching can also induce the consequence of the existence of a high number of possible final states.

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Acknowledgements

The author thanks the anonymous reviewers for their helpful comments and suggestions, which led to an improvement of this paper. Some computations have been made using the Software DYNAMICS [32]. This work was supported by the National Natural Science Foundation of China (No. 11002092).

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

    Yongxiang Zhang

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Correspondence to Yongxiang Zhang.

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Zhang, Y. Switching-induced Wada basin boundaries in the Hénon map. Nonlinear Dyn 73, 2221–2229 (2013). https://doi.org/10.1007/s11071-013-0936-2

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