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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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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