Efficient bifurcation analysis of periodically-forced distributed parameter systems

Changes in the qualitative features of the bifurcation diagrams or the dyna mic features of forced periodic systems occur at singular points, which sat isfy certain defining conditions. The loci of these singular points may be constructed by a continuation procedure and used to bound parameter regions with qualitatively different features. When the model of a forced periodic system is a set of partial differential equations, construction of these l oci may require extensive computational time, making this task often imprac tical. We present here a novel, very efficient numerical method for constru ction of these loci. The procedure uses Frechet differentiation to simplify the determination of the defining conditions and the Broyden inverse updat e method to accelerate the iterative steps involved in the shooting method. The procedure is illustrated first by construction of a map of parameter r egions with qualitatively different bifurcation diagrams for an adiabatic r everse-flow reactor (RFR), the direction of feed to which is changed period ically. We then construct a map of parameter regions in which a cooled RFR has qualitatively different dynamic features. Both maps reveal surprising f eatures. (C) 2000 Elsevier Science Ltd. All rights reserved.