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Degenerate Hopf instability in oscillatory reaction-diffusion equations

Pages: 784 - 793, Issue Special, September 2007

 Abstract        Full Text (462.3K)              

Toshi Ogawa - Graduate school of Engineering Science, Osaka University, Toyonaka, 560-8531, Japan (email)

Abstract: Degenerate critical points on a 2-compnent reaction diffusion system with a global inhibition (GI) are studied. They can be an organizing center for a variety of spatially non-uniform oscillations. The Hopf-bifurcation point for the 0-mode oscillation (spatially uniform oscillation) is controlled by the strength of GI so that the eairlier destabilization of the higher mode oscillations can happen.

Keywords:  Degenerate Hopf bifurcation, normal form, rotating wave, standing wave.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: September 2006;      Revised: May 2007;      Published: September 2007.