HOPF bifurcation in a CSTR using characteristic LOCI

Abstract

The richness of the dynamic behavior of a single first order reaction carried out in a stirred tank reactor is well known: different topological configurations associated with changes in system parameters appear in the phase plane. In this paper, the existence of stable or unstable limit cycles is studied from a different point of view. Hopf Bifurcation is treated with the approach of feedback systems and harmonic balance for predicting the existence of limit cycles, giving approximations on their amplitude and frequency as well as giving stability results. The great development in frequency domain techniques in the last years makes it possible to analyse the classical bifurcation problem using characteristic loci. The problem is reduced to a simple graphical one, where the solution is obtained at the intersection—if it exists—between the characteristic loci (linear part) and a vector (nonlinear part).