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. (C) 2008 American Institute of Physics.