The main pseudo-steady states in the process of catalytic hydrogen peroxide decomposition are analysed. The dominant steady states during the monotonic and oscillatory evolution, well known experimentally, are defined by stoichiometric network analysis of the model for this process. The trajectories for the evolution of the system in the phase space in the vicinity of the unstable pseudo-steady state where oscillatory behaviour is obtained, are also calculated. The adjustment of the phase trajectory to the corresponding oscillation is proposed as an additional criterion for the selection of the kinetic parameters necessary for numerical simulation. The calculation procedure is general, independent of the model under consideration.

Detailed dynamics of the hypothalamic-pituitary-adrenal (HPA) axis is complex, depending on the individual metabolic load of an organism, its current status (healthy/ill, circadian phase (day/night), ultradian phase) and environmental impact. Therefore, it is difficult to compare the HPA axis activity between different individuals or draw unequivocal conclusions about the overall status of the HPA axis in an individual using single time-point measurements of cortisol levels. The aim of this study is to identify parameters that enable us to compare different dynamic states of the HPA axis and use them to investigate self-regulation mechanisms in the HPA axis under acute and chronic stress. In this regard, a four-dimensional stoichiometric model of the HPA axis was used. Acute stress was modeled by inducing an abrupt change in cortisol level during the course of numerical integration, whereas chronic stress was modeled by changing the mean stationary state concentrations of CRH. Effects of acute stress intensity, duration and time of onset with respect to the ultradian amplitude, ultradian phase and the circadian phase of the perturbed oscillation were studied in detail. Bifurcation analysis was used to predict the response of the HPA axis to chronic stress. Model predictions were compared with experimental findings reported in the literature and relevance for pharmacotherapy with glucocorticoids was discussed.