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

  • Giani Egaña Fernández
  • J Sarría González
  • Mariano Rodríguez RicardEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 275)


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.


Turing instability Hopf bifurcation Reaction diffusion Twinkling pattern 



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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Giani Egaña Fernández
    • 1
  • J Sarría González
    • 2
  • Mariano Rodríguez Ricard
    • 1
    Email author
  1. 1.Facultad de Matemática y Computación, San Lázaro y L, VedadoUniversidad de La HabanaHavanaCuba
  2. 2.Facultad 4Universidad de Ciencias InformáticasHavanaCuba

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