Computers & Chemical Engineering, Vol.121, 639-645, 2019
Direct computation of Hopf bifurcation points in differential-algebraic equations
In this work, we address the bifurcation theory for differential-algebraic equations (DAEs). Our main subject is the direct computation of Hopf bifurcation points, for which we present a novel methodology. In order to achieve this goal, the theory of ordinary differential equations (ODEs) was extended to formulate a concise stability criterion and provide a procedure for the computation of characteristic polynomials of DAEs. Hopf bifurcation points of DAE models of any index and with any number of parameters can now be easily handled. The methodology is tested for the calculation of Hopf bifurcation points of a benchmark model in chemical engineering in a fast and accurate way. (C) 2018 Elsevier Ltd. All rights reserved.