Satnoianu, R. A. and Maini, P. K. and Menzinger, M. (2001) Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity. Physica D, 160 (1-2). pp. 79-102.
new type of instability in coupled reaction-diffusion-advection systems is analysed in a one-dimensional domain. This instability, arising due to the combined action of flow and diffusion, creates spatially periodic stationary waves termed flow and diffusion-distributed structures (FDS). Here we show, via linear stability analysis, that FDS are predicted in a considerably wider domain and are more robust (in the parameter domain) than the classical Turing instability patterns. FDS also represent a natural extension of the recently discovered flow-distributed oscillations (FDO). Nonlinear bifurcation analysis and numerical simulations in one-dimensional spatial domains show that FDS also have much richer solution behaviour than Turing structures. In the framework presented here Turing structures can be viewed as a particular instance of FDS. We conclude that FDS should be more easily obtainable in chemical systems than Turing (and FDO) structures and that they may play a potentially important role in biological pattern formation.
|Uncontrolled Keywords:||Flow-distributed structures (FDS); Flow-distributed oscillations (FDO); Differential-flow instability (DIFI); Turing instability; Stationary space-periodic patterns; Hopf instability; Quadratic and cubic autocatalysis|
|Subjects:||A - C > Biology and other natural sciences|
|Research Groups:||Centre for Mathematical Biology|
|Deposited By:||Philip Maini|
|Deposited On:||20 Nov 2006|
|Last Modified:||20 Jul 2009 14:21|
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