Abstract
We report a startling mosaic-like organization of stability phases found in the low-frequency limit of a driven Brusselator. Such phases correspond to periodic oscillations having a constant number of spikes per period. The mosaic is free from chaotic oscillations and is formed by an apparently infinite cascade of oscillations whose number of spikes grow without bound. Wide windows free from chaos but supporting unbounded quantities of complex oscillations are potentially of interest to operate driven oscillators such as lasers, electronic circuits, and biochemical pacemakers.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E.N. Lorenz, J. Atmos. Sci. 49, 2449 (1992)
J. Argyris, G. Faust, M. Haase, R. Friedrich, An Exploration of Dynamical Systems and Chaos, 2nd edn. (Springer, New York, 2015)
S. Strogatz, Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering, 2nd Edition, (Westview Press, Boulder, 2015)
J.A.C. Gallas, Mod. Phys. Lett. B 29, 1530018 (2015). Chapter in Peregrinations from Physics to Phylogeny: Essays on the Occasion of Hao Bailin’s 80 Birthday, Edited by K.K. Phua, M. Ge (World Scientific, Singapore, 2016)
R. Kremann, Die periodischen Erscheinungen in der Chemie (F. Enke Verlag, Stuttgart, 1913)
E.S. Hedges, J.E. Myers, The Problem of Physico-Chemical Periodicity (Arnold & Co, London, 1926)
A. Lotka, Z. Phys. Chem. 72, 508 (1910)
J. Hirniak, Z. Phys. Chem. 75, 675 (1910)
A.J. Lotka, Z. Phys. Chem. 80, 159 (1912)
D. Aubin, A.D. Dalmedico, Hist. Math. 29, 273 (2002)
K. Tomita, T. Kai, F. Hikami, Prog. Theor. Phys. 57, 1159 (1977)
C. Knudsen, J. Sturis, J.S. Thomsen, Phys. Rev. A 44, 3503 (1991)
K. Tomita, Phys. Rep. 86, 113 (1982)
B.L. Hao, Elementary Symbolic Dynamics and Chaos in Dissipative Dynamical Systems (World Scientific, Singapore, 1989)
B.-L. Hao, W.-M. Zheng, Applied Symbolic Dynamics and Chaos (World Scientific, Singapore, 1989)
B. Hao, W. Zheng, Applied Symbolic Dynamics and Chaos, 2nd revised edn. (Peking University Press, Beijing, 2014)
J.A.C. Gallas, Adv. Atom. Mol. Opt. Phys. 65, 127 (2016)
L. Junges, J.A.C. Gallas, J. Opt. Soc. Am. B 33, 373 (2016)
J.G. Freire, R. Meucci, F.T. Arecchi, J.A.C. Gallas, Chaos 25, 097607 (2015)
L. Junges, J.A.C. Gallas, Opt. Comm. 285, 4500 (2012)
L. Junges, J.A.C. Gallas, New J. Phys. 17, 053038 (2015)
J.G. Freire, J.A.C. Gallas, Phys. Chem. Chem. Phys. 13, 12191 (2011)
J.G. Freire, J.A.C. Gallas, Phys. Lett. A 375, 1097 (2011)
M.R. Gallas, M.R. Gallas, J.A.C. Gallas, Eur. Phys. J. Special Topics 223, 2131 (2014)
A. Sack, J.G. Freire, E. Lindberg, T. Pöschel, J.A.C. Gallas, Sci. Rep. 3, 03350 (2013)
E. Pugliese, R. Meucci, S. Euzzor, J.G. Freire, J.A.C. Gallas, Sci. Rep. 5, 08447 (2015)
J.G. Freire, R.J. Field, J.A.C. Gallas, J. Chem. Phys. 131, 044105 (2009)
M.A. Nascimento, J.A.C. Gallas, H. Varela, Phys. Chem. Chem. Phys. 13, 441 (2011)
J.G. Freire, C. Cabeza, A. Marti, T. Pöschel, J.A.C. Gallas, Sci. Rep. 3, 1958 (2013)
J.G. Freire, C. Cabeza, A. Marti, T. Pöschel, J.A.C. Gallas, Eur. Phys. J. Special Topics 223, 2857 (2014)
V. Kovanis, A. Gavrielides, J.A.C. Gallas Eur. Phys. J. D 58, 181 (2010)
M.J.B. Hauser, J.A.C. Gallas, J. Phys. Chem. Lett. 5, 4187 (2014)
M.R. Gallas, J.A.C. Gallas, Chaos 25, 064603 (2015)
R.J. Field, J.A.C. Gallas, D. Schuldberg, Comm. Nonlin. Sci. Num. Sim. 49, 135 (2017)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Freire, J.G., Gallas, M.R. & Gallas, J.A.C. Stability mosaics in a forced Brusselator. Eur. Phys. J. Spec. Top. 226, 1987–1995 (2017). https://doi.org/10.1140/epjst/e2017-70020-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2017-70020-x