Reaction Kinetics, Mechanisms and Catalysis

, Volume 111, Issue 2, pp 431–442 | Cite as

Linear diffusive feed approach to explaining long range activation induced oscillations

  • István Szalai


The spatiotemporal dynamics of a single step cubic autocatalytic reaction, \(\hbox{A} + \hbox{2B} \mathop{\rightarrow}\limits^{k} \hbox{3B}\), in an open one-side-feed reactor is studied numerically. This system is capable of showing spatiotemporal oscillations if the diffusivity of B is faster than that of the A as a result of the anisotropy of the reactor. We apply a linear diffusive feed approach to describe this phenomenon and show that the results of the approximate method is in reasonable agreement with the exact modeling by using mixed boundary conditions. The analysis of the approximate model points out that the instability is governed by the faster removal of B compare to the feed of A. The instability appears when the diffusion coefficient of B more than twice larger than that of A, but stable oscillations develop at even larger difference. The linear diffusive feed model with cubic autocatalysis shows similarities with the Gray–Scott model, where an additional chemical reaction provides the necessary higher removal rate of the activator.


Nonlinear dynamics Oscillatory reactions Autocatalysis Patten formation 



We thank Patrick De Kepper and Pierre Borckmans for fruitful discussions, and the support of the Hungarian Scientific Research Fund (OTKA 77986, 100891).


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2013

Authors and Affiliations

  1. 1.Laboratory of Nonlinear Chemical Dynamics, Institute of ChemistryEötvös UniversityBudapestHungary

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