February  2002, 2(1): 129-147. doi: 10.3934/dcdsb.2002.2.129

Identification of modulated rotating waves in pattern-forming systems with O(2) symmetry


Department of Mathematics, San Diego State University, San Diego, CA 92182, United States

Received  April 2001 Revised  October 2001 Published  November 2001

A numerical algorithm for identifying Modulated Rotating Waves in spatially extended systems with O(2) symmetry—the symmetry group of rotations and reflections on the plane, is presented. The algorithm can be applied to numerical simulations of Partial Differential Equations (PDEs) and experimental data obtained in a laboratory. The basic methodology is illustrated with various cellular patterns obtained from video images of a combustion experiment carried out on a circular burner. Rotating waves and modulated rotating waves are successfully identified in the experiment. The algorithm is then validated by comparing the analysis of experimental patterns with the analysis of computational patterns obtained from numerical simulations of a reaction-diffusion PDE model.
Citation: A. Palacios. Identification of modulated rotating waves in pattern-forming systems with O(2) symmetry. Discrete & Continuous Dynamical Systems - B, 2002, 2 (1) : 129-147. doi: 10.3934/dcdsb.2002.2.129

Cicely K. Macnamara, Mark A. J. Chaplain. Spatio-temporal models of synthetic genetic oscillators. Mathematical Biosciences & Engineering, 2017, 14 (1) : 249-262. doi: 10.3934/mbe.2017016


Qigang Yuan, Jingli Ren. Periodic forcing on degenerate Hopf bifurcation. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2857-2877. doi: 10.3934/dcdsb.2020208


Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367


Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311


Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1717-1746. doi: 10.3934/dcdss.2020451


Yahui Niu. A Hopf type lemma and the symmetry of solutions for a class of Kirchhoff equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021027


W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349


Alexey Yulin, Alan Champneys. Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1341-1357. doi: 10.3934/dcdss.2011.4.1341


John Leventides, Costas Poulios, Georgios Alkis Tsiatsios, Maria Livada, Stavros Tsipras, Konstantinos Lefcaditis, Panagiota Sargenti, Aleka Sargenti. Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021004


Hirofumi Notsu, Masato Kimura. Symmetry and positive definiteness of the tensor-valued spring constant derived from P1-FEM for the equations of linear elasticity. Networks & Heterogeneous Media, 2014, 9 (4) : 617-634. doi: 10.3934/nhm.2014.9.617

2019 Impact Factor: 1.27


  • PDF downloads (30)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]