Infinite period and Hopf bifurcations for the pH-regulated oscillations in a semibatch reactor (H2O2–Cu2+–S2O2−3–NaOH system)

Abstract

Dynamic behavior of the pH-regulated oscillations has been studied for the hydrogen peroxide oxidation of thiosulfate ions in the presence of trace amounts of copper(II) ions in a semibatch reactor. A solution of 0.08 M Na(2)S(2)O(3) and 0.112 M NaOH was flowed at 0.160 mL/min into 300 mL of solution containing the H(2)O(2) and Cu(2+) in a vessel. There exists a critical value of the H(2)O(2) or Cu(2+) concentrations below which the system does not oscillate. The oscillations appear due to an infinite period bifurcation at low initial concentrations of the H(2)O(2). The initial concentration of Cu(2+) may be considered as a bifurcation parameter in this case. Increase of the initial hydrogen peroxide concentration causes the pH-regulated oscillations through a nondegenerate supercritical Hopf bifurcation. The classification of bifurcations is based on the analysis of the behavior of oscillation amplitude and period at different initial concentrations of the H(2)O(2) and Cu(2+). Our results show a possibility to distinguish different scenarios for the appearance of transient oscillations in semibatch experiments. (c) 1996 American Institute of Physics.

Relaxation to Equilibrium Can Be Hindered by Transient Dissipative Structures

“…However, oscillatory behaviors or spatial pattern formations can be observed as transient phenomena during the course of relaxation to equilibrium [5][6][7][8][9]11,12]. Here, we address the following question: Can the formation of (transient) dissipative structures make far-from-equilibrium conditions last significantly longer by slowing down the relaxation process to equilibrium?…”

The effect of oxygen on time-dependent bifurcations in the Belousov–Zhabotinsky oscillating chemical reaction in a batch

“…Qualitative analysis of time dependences of oscillation attributes at low and high oxygen concentrations suggests that at low oxygen concentrations oscillations disappear through the time-delayed Hopf bifurcation. 32,33 At high oxygen concentrations they disappear through the saddle node infinite period (SNIPER) bifurcation. 34 In the middle range of the oxygen concentrations (30-50%) we found that oscillations may disappear either through the time-depended Hopf or SNIPER bifurcations in unpredictable manner.…”

“…Time-delayed Hopf bifurcation 32,33,36,37 In this case oscillations disappear through oscillations with finite period and zero amplitude. Time dependences of oscilla-tion period and amplitude are characterized by the following laws in a vicinity of the moment of time when oscillations disappear: 32…”

Dynamic transitions in a model of the hypothalamic-pituitary-adrenal axis

“…In order to investigate the contribution of individual reaction steps to the overall dynamics and characterize bifurcation types in the model, two methods were applied: the method of numerical continuation [43][44][45][46][47] and the method proposed by Maselko 48 and other authors [61][62][63][64][65][66][67][68][69][70][71][72][73][74][75] for examination of bifurcations in oscillatory chemical reaction systems. The numerical continuation method was applied to each rate constant separately, keeping all other rate constants fixed.…”