Structures of chaos in open reaction systems.

By numerically simulating the Bray-Liebhafsky (BL) reaction (the hydrogen peroxide decomposition in the presence of hydrogen and iodate ions) in a continuously fed well stirred tank reactor (CSTR), we find "structured" types of chaos emerging in regular order with respect to flow rate as the control parameter. These chaotic "structures" appear between each two successive periodic states, and have forms and evolution resembling to the neighboring periodic dynamics. More precisely, in the transition from period-doubling route to chaos to the arising periodic mixture of different mixed-mode oscillations, we are able to recognize and qualitatively and quantitatively distinguish the sequence of "period-doubling" chaos and chaos consisted of mixed-mode oscillations (the "mixed-mode structured" chaos), both appearing in regular order between succeeding periodic states. Additionally, between these types of chaos, the chaos without such recognizable "structures" ("unstructured" chaos) is also distinguished. Furthermore, all transitions between two successive periodic states are realized through bifurcation of chaotic states. This scenario is a universal feature throughout the whole mixed-mode region, as well as throughout other mixed-mode regions obtained under different initial conditions.

The chaotic sequences in the Bray-Liebhafsky reaction in an open reactor.

Attractor reconstruction is done from the time series obtained by experimental investigation and by deterministic and stochastic simulation of the Bray-Liebhafsky oscillatory reaction. The appearance of deterministic chaos is confirmed and proven by both simulation and experiment, determining Lyapunov exponents for the sequences of flow rate values, as the control parameter. Moreover, unusual chaotic series were additionally recorded in the experiments, which cannot be found in deterministic numerical simulations. Therefore, an explanation of the difference between the dynamic behavior in the experiment and the deterministic simulation was sought and stochastic simulations based on the same reaction model were particularly useful. The fine structure of the chaotic windows, derived from the analysis of deterministic simulations in the range of flow rate values, made the system highly susceptible to noise induced effects, in general.