Numerical Simulation of the Behaviors of the Bray-Liebhafsky Oscillating Chemical Reaction by a Four-variable Model

Abstract

Based on a ten-step chemical model involving the concentrations of I<sub>2</sub>(aq), O<sub>2</sub>(aq), and the intermediates of I<sup>-</sup> and HIO<sub>2</sub>, four independent variables and seven irreversible steps, the nonlinear behavior of Bray-Liebhafsky (BL) oscillating reaction was investigated. The results showed that with different values of initial concentrations of reactants in the process of simulation, both periodic oscillation and chaotic behavior could be observed. In addition, at the same initial concentrations and rate constants, the system becomes more and more regular after being chaos. That is to say, the translation from chaos to periodic oscillation at the same initial conditions appeared in the BL system. The nonlinear behavior of system was also investigated briefly

A mathematical model of the Bray–Liebhafsky reaction

“…When the RGY model was first presented it was suggested that the system might be chaotic. It was argued that chaos is present due to the existence of large positive Lyapunov exponents [14]. (A Lyapunov exponent is a quantitative measurement of a dynamical system which characterizes the rate at which nearby trajectories converge or diverge asymptotically.…”

“…Various candidate reaction mechanisms have been proposed and these include those by Treindl & Noyes [11] and Schmitz [12,13]. Ren et al [14,15] developed a new mechanism by reducing a set of equations originally proposed by Kolar-Anić et al [16] and modified by Kissimonová et al [17] by ignoring the reversibility of some steps. This led to the set of ten chemical equations given by…”

“…A more recent effort to describe the dynamics of the Bray-Liebhafsky reaction was provided by Ren et al [14] (henceforth referred to as the 'RGY' model). This model reduces the 10 component reaction mechanism (1.3) to a set of seven equations given by…”

“…Various candidate reaction mechanisms have been proposed and these include those by Treindl & Noyes [11] and Schmitz [12,13]. Ren et al [14,15] developed a new mechanism by reducing a set of equations originally proposed by Kolar–Anić et al [16] and modified by Kissimonová et al [17] by ignoring the reversibility of some steps. This led to the set of ten chemical equations given by right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtrueI−+normalIO3−+2H+⟶normalHIO+HIO2, right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtrueHIO2+I−+H+⟶I2normalO+H2normalO, right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtrueI2normalO+H2normalO⟶2normalHIO, right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtruenormalHIO+I−+H…”

“…A more recent effort to describe the dynamics of the Bray–Liebhafsky reaction was provided by Ren et al [14] (henceforth referred to as the ‘RGY’ model). This model reduces the 10 component reaction mechanism (1.3) to a set of seven equations given by right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtrueA(aq)+V(aq)+2H(aq)→+0.611em0.278em.15emk1U(aq)+P(aq) right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtrueU(aq)+V(aq)+H(aq)→+0.611em0.278em.15emk22P(aq) right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtrueB(aq)+U(aq)→+0.611em0.278em.15emk32U(aq)+Z(aq)+…”