Numerical Hopf Bifurcation Techniques and the Dynamics of the Tubular Reactor Model

摘要

Numerical bifurcation techniques were developed for studying the multiplicity, stability, and oscillatory dynamics of the non-adiabatic tubular reactor with a single A yields B reaction. The techniques illustrate the existence of one, three, five, or seven steady states and bifurcating periodic solutions. We present numerical procedures for computing the Hopf bifurcation formulas which can determine the stability and location of the oscillation without integrating the parabolic partial differential equations. The combination of our Hopf techniques with steady state bifurcation methods enables us to determine all possible steady and stable oscillatory solutions exhibited by distributed parameter models such as the tubular reactor. (Author)