Jump transition due to a time-dependent bifurcation parameter in the bistable ioadate–arsenous acid reaction

Abstract

Bifurcation or limit point problems with slowly varying parameters are of interest in many research areas. Typically, the time dependency of the bifurcation parameter introduces a delay in the transition from one type of solution to the other. In this article, we study both theoretically and experimentally the bistable iodate–arsenous acid reaction when subjected to a time-dependent bifurcation parameter. This problem is tractable analytically and allows us to derive an expression for the transition delay with respect to the static bifurcation point as a function of the dimensionless ramping rate ε. For small and moderate values of ε, we predict that the delay is proportional to εp where the exponent p=2/3≈0.67. For the experimental conditions considered in this paper, our experimental data yield p=0.63±0.10.