The chaotic sequences in the Bray–Liebhafsky reaction in an open reactor

Abstract

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.

Iodine oxidation by hydrogen peroxide in acidic solutions, Bray-Liebhafsky reaction and other related reactions

“…The iodine oxidation by hydrogen peroxide is a component of the oscillating decomposition (D) of hydrogen peroxide catalysed by iodate in acidic solutions, known as the Bray-Liebhafsky (BL) reaction. [1][2][3][4][5][6][7][8][9][10][11][12] 2 H 2 O !…”

Dynamic behavior of the bray-liebhafsky oscillatory reaction controlled by sulfuric acid and temperature

“…However, on the basis of the obtained unusual chaotic series, it is impossible to determine the "route to chaos." Fur thermore, we know from model simulations [12][13][14][15] that some of existing chaotic states occur within such a small domain of the control parameter values caus ing that experimental quantification of them is impos sible, because stochastic fluctuations in the control bifurcation parameter drive dynamics among neigh boring periodic states and chaotic regime. Thus, experimental obtained data should be analyzed using the tools of dynamic system theory [41][42][43][44] Recently [9] we studied dynamic states of the BL reaction when sulfuric acid is the control parameter under the following conditions: T = 56.0°C, [KIO 3 ] 0 = 5.90 × 10 -2 mol l -1 , [H 2 O 2 ] 0 = 1.50 × 10 -1 mol l -1 , j 0 = 2.95 × 10 -2 min -1 and the inflow concentration of sul furic acid varied from [H 2 SO 4 ] = 4.22 × 10 -2 to 9.00 × 10 -2 mol l -1 .…”

“…In the latter, the stable non equilibrium stationary states, simple periodic oscillations, complex oscillations, bursts and deterministic chaos are discovered. These examinations have numerous intentions, from theo retical investigations and modeling [3,[11][12][13][14][15][16]] of the considered system or related ones, to their application in analytical purposes with the aim to measure con centrations below current detection limits [31][32][33][34], or to depict kinetic characterizations of catalysts [8,[35][36][37][38]. Therefore, the dynamic states under various com binations of control parameters must be examined which is also the case in this paper.…”

Numerical Simulation of the Behaviors of the Bray-Liebhafsky Oscillating Chemical Reaction by a Four-variable Model

“…Moreover, the Largest Lyapunov exponent for the former is 0.7359, whereas for the later is only 0.2015. In fact, experimental results in references showed that complex dynamic behavior, including transition from simple periodic oscillations to complex mixed-mode oscillations and chaos were observed by varying different parameters in CSTR [23,24]. The reason for appearing this complex phenomena in the nonlinear BL system is that although the whole system is far away from equilibrium, the relationship among each elementary reactions are weak and unstable factors are dominant and the behavior of the system is chaos.…”