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Competition of spiral waves in heterogeneous CGLE systems

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Abstract

The effects of spatial heterogeneity on a two-dimensional complex Ginzburg–Landau equation model are studied. In general, the interaction of a pair of spiral waves with a large degree of heterogeneity in two different media will cause three different patterns: (a) Multiple spiral waves coexist in different media; (b) the spiral wave is swept away in one medium and remains in another medium; (c) all of the spiral waves are suppressed by travelling waves having different frequencies. These travelling waves are generated from interface reported before. It is found that the interface is a wave source that can generate travelling waves with different frequencies in two submedia to compete with the original spiral waves in two different media. The competition results depend on the frequencies of the original spiral wave and the two travelling waves. Furthermore, local periodic pacing can replace the effect of the interface and reproduce the corresponding results, which gives additional evidence that the interface works as a wave source. The results give new ideas in pattern control such that we can suppress and annihilate spiral waves by generating a large degree of heterogeneity using selected parameters.

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Acknowledgements

The work is supported by the National Natural Science Foundation of China (Grant Nos. 11775020, 61573065 and 71731002).

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Authors and Affiliations

  1. School of Systems Science, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Chunli Huang, Xiaohua Cui & Zengru Di

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  1. Chunli Huang
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  2. Xiaohua Cui
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Correspondence to Xiaohua Cui.

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Huang, C., Cui, X. & Di, Z. Competition of spiral waves in heterogeneous CGLE systems. Nonlinear Dyn 98, 561–571 (2019). https://doi.org/10.1007/s11071-019-05212-1

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