Bifurcation from excitability to limit cycle oscillations at the end of the induction period in the classical Belousov–Zhabotinsky reaction

Dynamical attributes of nanocatalyzed self-oscillating reactions via bifurcation analyses

Self-oscillating chemical reactions that undergo reaction-diffusion (RD) phenomena have shown great potential for designing stimuli-responsive materials. Belousov-Zhabotinsky (BZ) reactions are one such class of reactions that exhibit nonlinear chemical oscillations due to redox cycles of the metal-ion catalyst by virtue of Hopf bifurcation. Using bifurcation analyses, here we investigate the BZ reactions, catalyzed by 0D-2D catalytic nanomats and bare nanosheets, which are known to exhibit enhanced dynamic response due to catalysts' heterogeneity. Specifically, we incorporate the nanocatalysts' activity in the kinetic model of the BZ reactions and, subsequently, use catalysts' activity as the bifurcation parameter for analyses. By computing higher-order Lyapunov and frequency coefficients, we have revealed new oscillatory regimes in the bifurcation diagram, including re-entrant regions where sustained oscillations are unexpectedly suppressed, even with high catalytic activity. In addition, we also calculate the amplitude and frequency of BZ oscillations in each of these regions as a function of nanocatalysts' activity. We believe that our current findings can be used to harness the nonlinearity of RD-based dynamical systems to provide unique functionalities to active stimuli-response systems.

Feed rate noise modulates autocatalysis and shapes the oscillations of the Belousov–Zhabotinsky reaction in a continuous stirred tank reactor

Noise applied to a specific reactant feed rate directs the Belousov–Zhabotinsky reaction into specific pathways and results in noise-controlled oscillation shapes and features.

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.

ENHANCEMENT AND RESTRICTION OF SYSTEM COORDINATION BY INTERACTION OF PATHWAYS

System coordination for a system with interaction of two pathways is investigated. Sufficient conditions for guaranteeing system coordination subject to any type, amplitude or period of external forcing are analytically derived. Effects of a pathway operating in the opposite direction on system coordination are examined in detail, and it is revealed that the pathway may enhance or restrict system coordination, depending on the values of kinetic parameters. It is concluded that increasing the complexity of enzymatic network by introducing interaction of pathways does not necessarily enhance system coordination. Numerical results using rectangular and sinusoidal forcing support the analytical results, and they quantitatively show how the system with interaction of two pathways maintain its coordination. When the sufficient conditions are satisfied, the system always develops to a finite stable (time-dependent) state under the forcing of any type, amplitude or period. When not, system coordination depends quantitatively on parameter values and the type, amplitude or period of external forcing. When two parameters are forced simultaneously, an additional factor, namely phase shifts between two forced parameters, also affects system coordination. It is shown that, unless the sufficient coordination conditions are maintained, external forcing may induce 'loss of coordination', resulting in the system having no biological functioning. The implications of the results for understanding biochemical coordination and for assessing possible consequences of modulating biochemical systems are discussed.