Limit cycles in the presence of convection: a traveling wave analysis.
We consider a diffusion model with limit cycle reaction functions. In an unbounded domain, diffusion spreads the pattern outwards from the source. Convection adds instability to the reaction-diffusion system. The result of this instability is a readiness to create a pattern. We choose the Lambda-Omega reaction functions for their simple limit cycle. We carry out a transformation of the dependent variables into polar form. From this we consider the initiation of the pattern to approximate a traveling wave. We carry out numerical experiments to test our analysis. These confirm the premise of the analysis, that the initiation can be modeled by a traveling wave. Furthermore, the analysis produces a good estimate of the numerical results. Most significantly, we confirm that the pattern consists of two different types.
Flach
E H
EH
Complex Systems, Indiana University School of Informatics, 1900 East Tenth Street, Eigenmann Hall 906, Bloomington, Indiana 47406, USA. flach@indiana.edu
Schnell
S
S
Norbury
J
J
D001683:Biological Clocks / Q000502:physiology*; D019521:Body Patterning / Q000502:physiology*; D003198:Computer Simulation; D008954:Models, Biological