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“Strong” Turing-Hopf Instability for Reaction-Diffusion Systems

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Book cover Analysis and Partial Differential Equations: Perspectives from Developing Countries

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 275))

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Abstract

Turing-Hopf instabilities for reaction-diffusion systems provide spatially inhomogeneous time-periodic patterns of chemical concentrations. In this presentation, it is shown the parameter space in which the reaction-diffusion system modelling glycolysis and the Lengyel-Epstein model could show twinkling patterns. To do so, we follow the Ricard-Mischler procedure in Ricard and Mischler (J Nonlinear Sci 19(5):467–496, 2009, [18]), i.e., considering this phenomenom as a consequence of the instability generated by diffusion on the limit cycle which appears due to a Hopf bifurcation about the spatially homogeneous steady state.

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Acknowledgments

Mariano Rodríguez Ricard would like to express his gratitude to the organizers of the ODA Week at Imperial College London (Nov 23-28, 2016), Prof. Michael Ruzhansky and Dr. Julio Delgado, for their support and cordiality during the workshop.

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Authors and Affiliations

  1. Facultad de Matemática y Computación, San Lázaro y L, Vedado, Universidad de La Habana, Havana, Cuba

    Giani Egaña Fernández & Mariano Rodríguez Ricard

  2. Facultad 4, Universidad de Ciencias Informáticas, Carretera a San Antonio Km 2 1/2, Havana, Cuba

    J Sarría González

Authors
  1. Giani Egaña Fernández
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  2. J Sarría González
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  3. Mariano Rodríguez Ricard
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Corresponding author

Correspondence to Mariano Rodríguez Ricard .

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Editors and Affiliations

  1. School of Mathematical Sciences, Queen Mary University of London, London, UK

    Julio Delgado

  2. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

    Michael Ruzhansky

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Egaña Fernández, G., Sarría González, J., Ricard, M.R. (2019). “Strong” Turing-Hopf Instability for Reaction-Diffusion Systems. In: Delgado, J., Ruzhansky, M. (eds) Analysis and Partial Differential Equations: Perspectives from Developing Countries. Springer Proceedings in Mathematics & Statistics, vol 275. Springer, Cham. https://doi.org/10.1007/978-3-030-05657-5_9

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