Parametric space for nonlinearly excited phase equation

Strunin, Dmitry V. ; Mohammed, Mayada Gassab

ANZIAM Journal, Tome 52 (2012), / Harvested from Australian Mathematical Society

Résumé

Slow variations in the phase of oscillators coupled by diffusion is generally described by a partial differential equation involving infinitely many terms. We consider the case of nonlocal coupling and numerically evaluate the ranges of parameters leading to different forms of a finite truncation of the equation, namely a form based on nonlinear excitation and a form based on linear excitation---the Kuramoto--Sivashinsky equation. References Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence. Springer--Verlag, Berlin, 1984. Kuramoto, Y. and Tsuzuki, T., Persistent propagation of concentration waves in dissipative media far from thermal equilibrium, Progr. Theor. Phys., 55, 1976, 356--369. doi:10.1143/PTP.55.356 Sivashinsky, G. I., Nonlinear analysis of hydrodynamical instability in laminar flames, Acta Astronaut., 4, 1977, 1177--1206. doi:10.1016/0094-5765(77)90096-0 Strunin, D. V., Autosoliton model of the spinning fronts of reaction, IMA J. Appl. Math., 63, 1999, 163--177. doi:10.1093/imamat/63.2.163 Strunin, D. V., Nonlinear instability in generalised nonlinear phase diffusion equation, Progr. Theor. Phys. Suppl., N 150, 2003, 444--448. doi:10.1143/PTPS.150.444 Strunin, D. V., Phase equation with nonlinear excitation for nonlocally coupled oscillators, Physica D: Nonlinear Phenomena, 238, 2009, 1909--1916. doi:10.1016/j.physd.2009.06.022 Tanaka, D. and Kuramoto, Y., Complex Ginzburg-Landau equation with nonlocal coupling, Phys. Rev. E, 68, 2003, 026219. doi:10.1103/PhysRevE.68.026219

Détail

Publié le : 2012-01-01
DOI : https://doi.org/10.21914/anziamj.v53i0.5065