Mixed-mode oscillations in a homogeneous pH-oscillatory chemical reaction system.
We examine experimentally a chemical system in a flow-through stirred reactor, which is known to provide large-amplitude oscillations of the pH value. By systematic variation of the flow rate, we find that the system displays hysteresis between a steady state and oscillations, and more interestingly, a transition to chaos involving mixed-mode oscillations. The basic pattern of the measured pH in the mixed-mode regime includes a large-scale peak followed by a series of oscillations on a much smaller scale, which are usually highly irregular and of variable duration. The bifurcation diagram shows that chaos sets in via a period-doubling route observed on the large-amplitude scale, but simultaneously small-amplitude oscillations are involved. Beyond the apparent accumulation of period doubling bifurcations, a mixed-mode regime with irregular oscillations on both scales is observed, occasionally interrupted by windows of periodicity. As the flow rate is further increased, chaos turns into quasiperiodicity and later to a simple small-amplitude periodic regime. Dynamics of selected typical regimes were examined with the tools of nonlinear time-series analysis, which include phase space reconstruction of an attractor and calculation of the maximal Lyapunov exponent. The analysis points to deterministic chaos, which appears via a period doubling route from below and via a route involving quasiperiodicity from above, when the flow rate is varied.
Bakes
Daniel
D
Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Institute of Chemical Technology, Prague, Technická 5, 166 28 Prague 6, Czech Republic.
Schreiberová
Lenka
L
Schreiber
Igor
I
Hauser
Marcus J B
MJ