Numerical experiments on the Turing instability in the Oregonator model

Numerical experiments on the Oregonator model of the Belousov-Zhabotinsky reaction with 2 variables (activator and inhibitor) are carried out. Influences of an inhibitory diffusion coefficient and inhibitory initial condition (concentration) on its pattern dynamics are studied for several values of a stoichiometric factor of the model. As a result, several pattern formation processes such as decrementally propagating waves and self replicating processes are found by changing the initial condition of the inhibitor and the stoichiometric factor under the Turing instability. In the self replicating process, new pattern dynamics acting as birth and death of waves is also found.

[1]  Reynolds,et al.  Dynamics of self-replicating patterns in reaction diffusion systems. , 1994, Physical review letters.

[2]  J. Keener,et al.  Spiral waves in the Belousov-Zhabotinskii reaction , 1986 .

[3]  A. Zhabotinsky,et al.  Dependence of Wave Speed on Acidity and Initial Bromate Concentration in the Belousov- Zhabotinsky Reaction-Diffusion System , 1994 .

[4]  R. M. Noyes,et al.  Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system , 1972 .

[5]  Dulos,et al.  Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern. , 1990, Physical review letters.

[6]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[7]  Self-organization in an excitable reaction-diffusion system: Synchronization of oscillatory domains in one dimension. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[8]  S. Kondo,et al.  A reaction–diffusion wave on the skin of the marine angelfish Pomacanthus , 1995, Nature.

[9]  N. H. Sabah,et al.  The effect of membrane parameters on the properties of the nerve impulse. , 1972, Biophysical journal.

[10]  H. Swinney,et al.  Experimental observation of self-replicating spots in a reaction–diffusion system , 1994, Nature.

[11]  Stefan Müller,et al.  Quantitative analysis of periodic chemotaxis in aggregation patterns of Dictyostelium discoideum , 1991 .

[12]  Shinji Koga,et al.  Localized Patterns in Reaction-Diffusion Systems , 1980 .

[13]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[14]  A. M. Zhabotinskii,et al.  Mechanism and mathematical model of the oscillating bromate-ferroin-bromomalonic acid reaction , 1984 .

[15]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.