Infinite period and Hopf bifurcations for the pH-regulated oscillations in a semibatch reactor (H(2)O(2)-Cu(2+)-S(2)O(2-) (3)-NaOH system)

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

Dynamic properties of a nonlinear five-dimensional stoichiometric model of the hypothalamic-pituitary-adrenal (HPA) axis were systematically investigated. Conditions under which qualitative transitions between dynamic states occur are determined by independently varying the rate constants of all reactions that constitute the model. Bifurcation types were further characterized using continuation algorithms and scale factor methods. Regions of bistability and transitions through supercritical Andronov-Hopf and saddle loop bifurcations were identified. Dynamic state analysis predicts that the HPA axis operates under basal (healthy) physiological conditions close to an Andronov-Hopf bifurcation. Dynamic properties of the stress-control axis have not been characterized experimentally, but modelling suggests that the proximity to a supercritical Andronov-Hopf bifurcation can give the HPA axis both, flexibility to respond to external stimuli and adjust to new conditions and stability, i.e., the capacity to return to the original dynamic state afterwards, which is essential for maintaining homeostasis. The analysis presented here reflects the properties of a low-dimensional model that succinctly describes neurochemical transformations underlying the HPA axis. However, the model accounts correctly for a number of experimentally observed properties of the stress-response axis. We therefore regard that the presented analysis is meaningful, showing how in silico investigations can be used to guide the experimentalists in understanding how the HPA axis activity changes under chronic disease and/or specific pharmacological manipulations.

Dynamic Instabilities and Mechanism of the Electrochemical Oxidation of Thiosulfate

The electrochemical oxidation of thiosulfate is revealed to have two distinct oscillatory regimes in both linear potential and galvanic voltammograms, where various nonlinear behaviors such as period-2, mixed-mode and quasi-periodic oscillations, and chaos are observed under potentiostatic or galvanostatic conditions. Electrochemical impedance spectroscopy and iR compensation characterization indicate that, depending on the operating conditions, the system could be either a strictly potentiostatic oscillator or an S-shaped negative differential resistance oscillator. Chronoamperometry measurements reveal that the first oscillatory process involves a single-electron transfer, whereas within the second oscillatory regime the average number of electrons transferred is around 3.8. Measurements with capillary electrophoresis and chemical methods illustrate that the oxidation products include S2O6(2-), S4O6(2-), S5O6(2-), S3O6(2-), and SO4(2-).

Relaxation to equilibrium can be hindered by transient dissipative structures

Relaxation processes in a closed chemical reaction-diffusion system which can potentially form Turing-like patterns during the transient are investigated to address the question given by the title. We find that when certain conditions are fulfilled the relaxation process is indeed drastically hindered, once the pattern is formed. This slowing down is shown to be due to stepwise relaxation, where each plateau in the relaxation process corresponds to residence at a certain spatial pattern. Mechanism and universality of the phenomena are discussed.