Period lengthening and associated bifurcations in a two‐variable, flow Oregonator

Intensity dependence of sub-harmonics in cortical response to photic stimulation

Objective. Periodic photic stimulation of human volunteers at 10 Hz is known to entrain their Electroencephalography (EEG) signals. This entrainment manifests as an increment in power at 10, 20, 30 Hz. We observed that this entrainment is accompanied by the emergence of sub-harmonics, but only at specific frequencies and higher intensities of the stimulating signal. Thereafter, we describe our results and explain them using the physiologically inspired Jansen and Rit Neural Mass Model (NMM).Approach. Four human volunteers were separately exposed to both high and low intensity 10 Hz and 6 Hz stimulation. A total of 4 experiments per subject were therefore performed. Simulations and bifurcation analysis of the NMM were carried out and compared with the experimental findings. <i> Main results. High intensity 10 Hz stimulation led to an increment in power at 5 Hz across all the 4 subjects. No increment of power was observed with low intensity stimulation. However, when the same protocol was repeated with a 6 Hz photic stimulation, neither high nor low intensity stimulation were found to cause a discernible change in power at 3 Hz. We found that the NMM was able to recapitulate these results. A further numerical analysis indicated that this arises from the underlying bifurcation structure of the NMM. <i> Significance. The excellent match between theory and experiment suggest that the bifurcation properties of the NMM are mirroring similar features possessed by the actual neural masses producing the EEG dynamics. Neural Mass Models could thus be valuable for understanding properties and pathologies of EEG dynamics, and may contribute to the engineering of brain-computer interface technologies.

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.