Jump transition due to a timehyphen;dependent bifurcation parameter in the bistable ioadatendash;arsenous acid reaction

摘要

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 iodatendash;arsenous acid reaction when subjected to a timehyphen;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 egr;. For small and moderate values of egr;, we predict that the delay is proportional to egr;pwhere the exponentp=2/3ap;0.67. For the experimental conditions considered in this paper, our experimental data yieldp=0.63plusmn;0.10.