Small-Amplitude and Mixed-Mode pH Oscillations in the Bromate−Sulfite−Ferrocyanide−Aluminum(III) System

Abstract

The BrO(3)(-)-SO(3)(2-)-Fe(CN)(6)(4-) (BSF) pH-oscillatory system is coupled to the Al(OH)(3) precipitation equilibrium (BSFA system) and studied in a stirred flow reactor. The dynamic behavior of the BSFA system differs significantly from that of the BSF system. In addition to the large-amplitude pH oscillations found in the BSF system, new small-amplitude and mixed-mode oscillations occur. A detailed mechanism of the BSFA system is developed and investigated.

Stern–Brocot trees in cascades of mixed-mode oscillations and canards in the extended Bonhoeffer–van der Pol and the FitzHugh–Nagumo models of excitable systems

“…Mixed-mode oscillation is a ubiquitous phenomenon studied profusely in experiments and models of prototypic dynamical systems in chemistry [1][2][3][4][5][6][7][8][9][10], physics [11][12][13][14][15], and neuroscience [16][17][18][19][20][21]. Mixed-mode oscillations (MMOs) are complex oscillatory patterns consisting of trains of small amplitude oscillations followed by large excursions of relaxation type.…”

Singular Hopf bifurcations and mixed-mode oscillations in a two-cell inhibitory neural network

“…Mixed-mode oscillations (MMOs) were observed in both experiments and models of systems from chemistry [1][2][3][4][5][6][7], physics [8,9] and neuroscience [10][11][12][13][14][15][16], and they are defined as complex oscillatory patterns consisting of small amplitude oscillations followed by large excursions of relaxation type, in each periodic cycle. For example, localized structures of large amplitude oscillations on a background of small amplitude oscillations were identified in experiments on the photosensitive Ru(bpy) 3 -catalyzed Belousov-Zhabotinsky reaction in a thin layer of silica gel with photochemical global negative feedback imposed through illumination [5]; in the neural system, MMOs were found in central pattern generators such as the lower brain stem network (the preBötzinger complex) that generates respiratory rhythm in mammals [11], or in electrophysiological (in vitro) studies of spiny stellate cells in layer II medial entorhinal cortex [10]; more recently, MMOs were also discovered in dusty plasmas [9].…”

Front propagation in the bromate–sulfite–ferrocyanide–aluminum (III) system: Autocatalytic front in a buffer system

“…where k 1 = 4.9 × 10 −2 M −1 s −1 (this work), k 2 = 44 M −1 s −1 (this work), k 3 = 8.5 × 10 −2 M −1 s −1 [9], k 4 = 5.5 × 10 −3 M −1 s −1 (this work), K S1 = 6.065 × 10 6 M −1 (log K S1 = 6.78), K S2 = 58.74 M −1 (log K S2 = 1.77) [19], K F = 12589 M −1 (log K F = 4.10) [20,21], K SA = 38.46 M −1 (log K SA = 1.585) [21]. Rate constants were de- ].…”

“…This system is composed of the well-known bromate-sulfite-ferrocyanide (BSF) [7] oscillatory reaction coupled to the Al(OH) 3 precipitation equilibrium [8,9]. We suggest that these patterns arise as the result of reversible coupling of free protons to large particles of precipitated Al(OH) 3 .…”

“…A large number of experiments run under different initial conditions allowed us to refine the values of k 1 , k 2 , and k 4 used in our previous paper[9] (namely 3.3 × 10 −2 M −1 s −1 , 22 M −1 s −1 and 0, respectively). The function Θ is defined as follows.If [Al(OH) + 2 ] > K p [H + ], Θ = 1.In this case, we assume that the precipitation-dissolution process is in quasi-equilibrium.…”