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Turing instability in reaction–diffusion models on complex networks

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  • Ide, Yusuke
  • Izuhara, Hirofumi
  • Machida, Takuya

Abstract

In this paper, the Turing instability in reaction–diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erdős–Rényi, the Watts–Strogatz, and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we numerically reveal that stable and unstable regions of a homogeneous steady state on the parameter space of two diffusion coefficients completely differ, depending on the network architecture. In addition, we theoretically discuss the stable and unstable regions in the cases of regular enhanced ring lattices which include regular circles, and networks generated by the threshold network model when the number of vertices is large enough.

Suggested Citation

  • Ide, Yusuke & Izuhara, Hirofumi & Machida, Takuya, 2016. "Turing instability in reaction–diffusion models on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 331-347.
    • Handle: RePEc:eee:phsmap:v:457:y:2016:i:c:p:331-347
    DOI: 10.1016/j.physa.2016.03.055
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    References listed on IDEAS

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    1. Yusuke Ide & Norio Konno & Naoki Masuda, 2010. "Statistical Properties of a Generalized Threshold Network Model," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 361-377, September.
    2. Malbor Asllani & Joseph D. Challenger & Francesco Saverio Pavone & Leonardo Sacconi & Duccio Fanelli, 2014. "The theory of pattern formation on directed networks," Nature Communications, Nature, vol. 5(1), pages 1-9, December.
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    Cited by:

    1. Kon, Ryusuke & Kumar, Dinesh, 2023. "Stability of Rosenzweig–MacArthur models with non-diffusive dispersal on non-regular networks," Theoretical Population Biology, Elsevier, vol. 150(C), pages 14-22.

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