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Pattern dynamics of a Gierer–Meinhardt model with spatial effects

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Abstract

Interactions of activator and inhibitor can be widely applied in different fields. As a result, dynamical behaviors of an activator–inhibitor model with different sources are investigated. We obtained the condition of Turing bifurcation by using linear stability analysis, and the amplitude equation by employing multiple scale analysis. Moreover, the stability of amplitude equation was presented. It turned out that the model can show spot patterns, stripe patterns and the coexistence of spot and stripe patterns. Numerical simulations well validate our theoretical analysis. Our results highlight the relationship between pattern formation and variation of biological tissues.

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Acknowledgements

The project is funded by the National Natural Science Foundation of China under Grants (11501338, 11671241 and 11301490), 131 Talents of Shanxi University, Program for the Outstanding Innovative Teams (OIT) of Higher Learning Institutions of Shanxi, and Natural Science Foundation of Shanxi Province Grant No. 201601D021002.

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Authors and Affiliations

  1. Complex Systems Research Center, Shanxi University, Shanxi, 030006, Taiyuan, People’s Republic of China

    Gui-Quan Sun & Cui-Hua Wang

  2. College of Life Sciences, Fujian Agriculture and Forestry University, Fuzhou, 350002, Fujian, People’s Republic of China

    Ze-Yan Wu

Authors
  1. Gui-Quan Sun
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  2. Cui-Hua Wang
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  3. Ze-Yan Wu
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Correspondence to Ze-Yan Wu.

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Sun, GQ., Wang, CH. & Wu, ZY. Pattern dynamics of a Gierer–Meinhardt model with spatial effects. Nonlinear Dyn 88, 1385–1396 (2017). https://doi.org/10.1007/s11071-016-3317-9

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  • DOI: https://doi.org/10.1007/s11071-016-3317-9

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