Bifurcation analysis of hopping behavior in cellular pattern-forming systems

International Journal of Bifurcation and Chaos

Volumn 17, Issue 2, 2007, Pages 509-520

  Palacios, Antonio ^a   Blomgren, Peter ^a   Gasner, Scott ^a  

^a SAN DIEGO STATE UNIVERSITY   (United States)

Author keywords

Bifurcation; Cellular flames; Spatio temporal patterns

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; NONLINEAR EQUATIONS; SYSTEM STABILITY;

CELLULAR FLAMES; HOPPING BEHAVIOR; SPATIO TEMPORAL PATTERNS; STEADY-STATE MODES;

CELLULAR NEURAL NETWORKS;

EID: 34248515419     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127407017380     Document Type: Article

References (24)

1. Armbruster, D., Guckenheimer, J. & Holmes, P. [1988] "Heteroclinic cycles and modulated traveling waves in systems with O(2) symmetry," Physica D 29, 257-282.
2. Blomgren, P., Gasner, S. & Palacios, A. [2005a] "Hopping behavior in the Kuramoto-Sivashinsky equation," Chaos 15, 013706.
3. Blomgren, P., Gasner, S. & Palacios, A. [2005b] "A stable second-order scheme for integrating the Kuramoto-Sivashiiisky equation in polar coordinates," Phys. Rev. E 72, 036701.
4. Campbell, S. & Holmes, P. [1991] "Bifurcation from O(2) symmetric heteroclinic cycles with three modes," Nonlinearity 4, 697-726.
5. Carbone, A., Gromov, M. & Prusinkiewicz, P. (eds.) [1998] Pattern Formation in Biology, Vision and Dynamics (World Scientific, Singapore).
6. Glazier, J. A. & Weaire, D. [1992] "The kinetics of cellular patterns," J. Phys.: Condens. Matter 4, 1867.
7. Gorman, M., el Hamdi, M. Pearson, B. &; Robbing, K. [1994a] "Ratcheting motion of concentric rings in cellular flames," Phys. Rev. Lett. 76, 228-231.
8. Gorman, M., el Hamdi, M. & Robbins, K. [1994b] "Experimental observations of ordered states of cellular flames," Combust. Sci. Tech. 98, 37-45.
9. Gorman, M., el Hamdi, M. & Robbins, K. [1994c] "Hopping motion in ordered states of cellular flames," Combust. Sci. Tech. 98, 71-78.
10. Gorman, M., el Hamdi, M. & Robbins, K. [1994d] "Rotating and modulated rotating states of cellular flames," Combust. Sci. Tech. 98, 25-35.
11. Gorman, M., Hamill, C., el Hamdi, M. & Robbins, K. [1994e] "Four types of chaotic dynamics in cellular flames," Combust. Sci. Tech. 98, 79-93.
12. Joulin, G. & Sivashinsky, G. [1983] "On the dynamics of nearly extinguished nonadiabatic cellular flames," Combust. Sci. Tech. 31, 75-90.
13. Karhunen, K. [1946] "Zur spektraltheorie stochasticher prozesse," Ann. Acad. Sci. Fennicae Ser. A 37, 3-76.
14. Kuramoto, Y. [1978] "Diffusion induced chaos in reaction systems," Progr. Theoret. Phys. Suppl. 64, 346-367.
15. Loève, M. [1955] Probability Theory (Van Nostrand, NY).
16. Lumley, J. [1967] "The structure of inhomogeneous turbulent flows," in Atmospheric Turbulence and Radio Wave Propagation, eds. Yaglom, A. & Tatarski, V. (Nauka, Moscow), pp. 166-178.
17. Palacios, A., Gunaratne, G., Gorman, M. & Robbins, K. [1997] "Cellular pattern formation in circular domains," Chaos 7, 463-475.
18. Palacios, A., Gunaratne, G., Gorman, M. & Robbins, K. [1998] "A Karhunen-Loève analysis of spatiotemporal flame patterns," Phys. Rev. E 57, 5958-5971.
19. Sirovich, L. [1987] "Turbulence and the dynamics of coherent structures, Part I: Coherent structures," Q. Appl. Math. XLV, 561-590.
20. Sivashinsky, G. [1977] "Nonlinear analysis of hydrodynamic instability in laminar flames, Part I: Derivation of basic equations," Acta Astraunica 4, 1177-1206.
21. Sivashinsky, G. [1980] "On flame propagation under conditions of stoichiometry," SIAM J. Appl. Math. 39, 67-82.
22. Sivashinsky, G. [1983] "Instabilities, pattern formation and turbulence in flames," Ann. Rev. Fluid Mech. 15, 179.
23. Tsimring, L. S. & Aranson, I. S. [1997] "Localized and cellular patterns in a vibrated granular layer," Phys. Rev. Lett. 79, 0031-9007.
24. Watson, G. [1962] A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge).