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Bifurcation analysis of reaction–diffusion Schnakenberg model

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Abstract

Bifurcations of spatially nonhomogeneous periodic orbits and steady state solutions are rigorously proved for a reaction–diffusion system modeling Schnakenberg chemical reaction. The existence of these patterned solutions shows the richness of the spatiotemporal dynamics such as oscillatory behavior and spatial patterns.

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Acknowledgments

We thank two anonymous reviewers for their helpful comments and suggestions.

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Authors and Affiliations

  1. Y.Y. Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, People’s Republic of China

    Ping Liu, Yuwen Wang & Xiuhong Feng

  2. Department of Mathematics, College of William and Mary, Williamsburg, VA, 23187-8795, USA

    Junping Shi

Authors
  1. Ping Liu
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  2. Junping Shi
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  3. Yuwen Wang
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  4. Xiuhong Feng
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Corresponding author

Correspondence to Ping Liu.

Additional information

Ping Liu: Partially supported by NSFC Grant 11101110 and NCET Grant 1251-NCET-002. Junping Shi: Partially supported by NSF Grant DMS-1022648. Yuwen Wang: Partially supported by NSFC Grant 11071051 and Natural Science Foundation of Heilongjiang Province of China A201106.

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Liu, P., Shi, J., Wang, Y. et al. Bifurcation analysis of reaction–diffusion Schnakenberg model. J Math Chem 51, 2001–2019 (2013). https://doi.org/10.1007/s10910-013-0196-x

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  • DOI: https://doi.org/10.1007/s10910-013-0196-x

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