Abstract
We study pattern formation induced by a spiral wave developing from heterogeneities in an excitable medium. Turbulence can be suppressed by a spiral wave from the heterogeneity, forming multiple coexistent systems of regular geometrical patterns. We find that the types of these patterns depend critically on the degree of heterogeneity. The underlying mechanism is due to dispersion relation which is characterized by excitability.
Similar content being viewed by others
References
M. C. Cross, P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)
A. T. Winfree, Science 175, 634 (1972)
A. T. Winfree, Science 181, 937 (1973)
A. T. Winfree, The Geometry of Biological Time (Springer, New York, 2001)
Q. Ouyang, J. M. Flesselles, Nature (London) 379, 143 (1996)
M. Kim et al., Science 292, 1357 (2001)
H. Zhang, Z. Cao, N. J. Wu, H. P. Ying, G. Hu, Phys. Rev. Lett. 94, 188301 (2005)
A. Pumir et al., Phys. Rev. Lett. 99, 208101 (2007)
S. Alonso, F. Sagues, A. S. Mikhailov, Science 299, 1722 (2003)
L. Glass, Phys. Today 49, No. 8, 40 (1996)
G. Bub et al., J. Cardiovasc. Electrophysiol. 14, 229 (2003)
J. N. Weiss et al., Circ. Res. 87, 1103 (2000)
A. T. Winfree, Science 266, 1003 (1994)
J. M. Starobin, J. I. Ziberter, E. M. Rusnak, C. F. Starmer, Biophys. J. 70, 581 (1996)
G. Bub, A. Shrier, Chaos 12, 747 (2002)
G. Bub, A. Shrier, L. Glass, Phys. Rev. Lett. 88, 058101 (2002)
G. Bub, A. Shrier, L. Glass, Phys. Rev. Lett. 94, 028105 (2005)
I. Schebesch, H. Engel, Phys. Rev. E 57, 3905 (1998)
F. G. Xie, Z. L. Qu, J. N. Weiss, A. Garfinkel, Phys. Rev. E 63, 031905 (2001)
R. Cassia-Moura, F. G. Xie, H. A. Cerdeira, Int. J. Bifurcation Chaos 14, 3363 (2004)
M. Bär, E. Meron, C. Utzny, Chaos 12, 204 (2002)
D. Pazo et al., Phys. Rev. Lett. 93, 168303 (2004)
X. Q. Zhou, H. Levine, Phys. Rev. E 47, R800 (1993)
K. ten Tusscher, A. V. Panfilov, Phys. Rev. E 68, 062902 (2003)
I. Aranson, H. Levine, L. Tsimring, Phys. Rev. Lett. 72 2561 (1994)
G. Bär, S. Sahle, J. S. Chen, A. A. Hoff, J. Chem. Phys. 110, 3251 (1999)
K. Agladze, M. W. Kay, V. Krinsky, N. Sarvazyan, Am J. Physiol. 293, H503 (2007)
H. Zhang, B. Hu, G. Hu, Phys. Rev. E 68, 026134 (2003)
Y. Q. Fu, H. Zhang, Z. Cao, B. Zheng, G. Hu, 72, 046206 (2005)
Q. Ouyang, H. L. Swinney, G. Li, Phys. Rev. Lett. 84, 1047 (2000)
M. Bär and M. Eiswirth, Phys. Rev. E 48, R1635 (1993)
M. Bär, et al., Chaos 4, 499 (1994)
W. Jahnke, A. T. Winfree, Int. J. Bifurcation Chaos 1, 445 (1991)
Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984)
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Chen, JX., Xu, JR., Zhang, XP. et al. Controlling chaos by developing spiral wave from heterogeneity in excitable medium. centr.eur.j.phys. 7, 108–113 (2009). https://doi.org/10.2478/s11534-008-0139-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s11534-008-0139-5