A model illustrating amplification of perturbations in an excitable medium
Field, Richard J.; Noyes, Richard M.
Журнал:
Faraday Symposia of the Chemical Society
Дата:
1974
Аннотация:
The oscillatory Belousovâ Zhabotinskii reaction can be modelled approximately by five irreversible steps: A + Y â X (M1), X + Y â P (M2), B + X â 2X + Z (M3), 2X â Q (M4), Z â Æ Y. (M5). These equations are based on the chemical equalities X = HBrO2, Y = Br<sup>â </sup>, Z = 2Ce(IV), and A = B = BrOâ 3. If the rate constants k M1 to k M4 are assigned by experimental estimates from oxybromine chemistry, the kinetic behaviour of the model depends critically upon the remaining parameters k M5 and Æ . When Æ does not differ too greatly from unity, and when k M5 is not too large, the steady state is unstable to perturbation and the system oscillates by describing a limit cycle trajectory.When Æ and k M5 lie outside the range of instability, the steady state is stable to very small perturbations. However, the steady state may still be excitable so that perturbation of the control intermediate Y by a few percent will instigate a single excursion during which concentrations of X, Y, and Z change by factors of about 10<sup>5</sup> before the system returns to the original steady state. This ability of a small perturbation of the steady state to trigger a major response by the system is just the type of behaviour necessary to explain the initiation of a trigger-wave by a heterogeneous â pacemakerâ as has been observed by Winfree. The same type of excitability of a steady state has important implications for the understanding of biochemical control mechanisms.
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