The stirred tank forced

We examine the response of a continuous stirred tank reactor (CSTR), in which a simple irreversible reaction A → B occurs, to periodic variations of the coolant temperature. The amplitude and the frequency of the forcing are used as control parameters. The remaining operating conditions are chosen so that the unforced CSTR exhibits a single stable oscillation; this means that for small forcing amplitudes the system behaves like a typical forced oscillator: its response consists of alternating entrainment and quasi-periodicity. As the forcing amplitude grows, more characteristic traits of the CSTR and the particular forcing variable become apparent, and a complicated picture develops, involving the co-existence of multiple periodic, quasi-periodic and even chaotic oscillations, period doublings and global bifurcations. We track several of these traits numerically, placing special emphasis on the mechanisms by which such features branch out from the well-defined low-amplitude region. Several algorithms based on shooting methods for boundary value problems are used in this task, and some appropriate ways of tackling the simple initial value problem of simulation are also employed. In particular, the need for efficient algorithms to tackle global bifurcations is stressed. Such algorithms seem to be indispensable tools in the systematic study of the forced CSTR and, more generally, of periodically forced oscillators. The qualitative traits discovered for the forced CSTR are compared with other known results for model systems, and several questions present themselves as possible subjects of further research, both for the CSTR and for a wide class of periodically forced and/or coupled reactor models.