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Parameter space analysis, pattern sensitivity and model comparison for Turing and stationary flow-distributed waves (FDS)

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Razvan Satnoianu, Philip K. Maini and Michael Menzinger

Editorial: Physica D, 160, p.79-102, 2001.


A 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.

Cuvinte cheie: Flow-distributed structures (FDS); Flow-distributed oscillations (FDO); Differential-flow instability (DIFI); Turing instability; Stationary space-periodic patterns; Hopf instability; Quadratic and cubic autocatalysis