Jump transition due to a time-dependent bifurcation parameter: An experimental, numerical, and analytical study of the bistable iodate–arsenous acid reaction

Abstract

We study the response diagram of the bistable iodate–arsenous acid reaction and investigate analytically and experimentally the jump transitions due to a time-dependent parameter. This parameter is changed linearly in time and its rate of change is characterized by a dimensionless parameter ε. We observe that the jump transition does not occur at a limit point of the steady states but is delayed. Asymptotic studies predict that this delay is proportional to an O(ε2/3) quantity as ε→0. The ε2/3 law is in agreement with the experimental observations of the transition between the lower and upper branches of steady states even if ε is not a small quantity [T. Erneux and J. P. Laplante, J. Chem. Phys. 90, 6129 (1989)]. In this paper, we investigate experimentally the second transition of the iodate–arsenous acid reaction, namely, the transition between the upper and lower branches of the steady states. We have found that the delay does not satisfy the ε2/3 law but rather is following an ε law. By comparing the experimental results and the results obtained from an analytical and numerical study of the bistable reaction, we show that the values of ε used in the experiments are too large to follow the ε2/3 law.