Inwardly rotating spiral wave breakup in oscillatory reaction-diffusion media

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Fagen Xie,¹ Dongzhu Xie,² and James N. Weiss³
¹Research Department, Kaiser Permanente, 100 S. Los Robles Ave, Pasadena, California 91101, USA
²Department of Physics, Shanghai Normal University, Shanghai 200233, People's Republic of China
³UCLA Cardiovascular Research Laboratory, Departments of Medicine (Cardiology) and Physiology, David Geffen School of Medicine at UCLA, Los Angeles, California 90095, USA

Received 19 August 2005; revised 14 March 2006; published 8 August 2006

Thebreakup of inwardly rotating spiral waves has been investigated inan oscillatory reaction-diffusion system near a Hopf bifurcation point. Thebreakup first occurred at the region far away from thecore area, then gradually involved the whole medium by increasingthe diffusion coefficient ratio between the two components of theoscillator system. With the approximation of the Complex-Ginzburg-Landau equation (CGLE),the criteria for the occurrence of the inwardly rotating spiralwave are examined theoretically. The analysis of the stability inthe corresponding CGLE revealed that the breakup of the inwardspiral wave was related to the Eckhaus instability.

URL:	http://link.aps.org/doi/10.1103/PhysRevE.74.026107
DOI:	10.1103/PhysRevE.74.026107
PACS:	82.40.Ck; 05.45.-a; 47.54.-r 82.40.Ck Pattern formation in chemical reactions with diffusion, flow and heat transfer 05.45.-a Nonlinear dynamics and nonlinear dynamical systems 47.54.-r Pattern selection; pattern formation YEAR: 2006
KEYWORDS:	rotational flow, waves, fluid oscillations, reaction-diffusion systems, chemically reactive flow, bifurcation, Ginzburg-Landau theory, flow instability