Slow relaxation oscillations in multi-scale adaptive next generation neural masses
Abstract
We have studied the mean field dynamics of heterogenous quadratic integrate-and-fire neurons in presence of spike frequency adaptation (SFA) by considering the exact formulation in terms of the next generation neural mass models (NG-NMMs). In particular, we have examined the emergence of slow relaxation oscillations in purely excitatory and excitatory-inhibitory NG-NMMs with SFA acting only on the excitatory population. Relaxation oscillations (ROs) connect low firing state (Down state) to high firing state (Up state) via the slow adaptation. In the examined cases, the orbit relaxes towards the Up State via a sequence of collective damped oscillations (peaks of activity), thus revealing population bursting dynamics. The slower is the adaptation time scale (the lower is the adaptation strength) the higher is the complexity (number of peaks) displayed by the relaxation oscillations. The increase in the number of peaks is due to spike-adding sequences controlled by the SFA parameters. The increase in the adaptation time scale leads to a chaos-induced spike-adding mechanism where the spike-adding occurs via intermediate chaotic transition regions. Quite peculiarly these chaotic regimes can be of two different types: Population Spiking and Population Bursting Chaos. The emergence of ROs with an increasing number of peaks, controlled by the adaptation strength, occurs via a different spike-adding mechanism. The ROs with (n + 1) peaks emerge through a saddle-node bifurcation, while coexisting, in a very narrow parameter region, with the solutions with n peaks, that looses stability via a sub-critical period doubling transition. In this case chaotic dynamics is not observable at the spike-adding bifurcations, but only in proximity of the population spiking-bursting transition. The considered NG-NMMs with SFA could be employed to interpret the results of neuro-physiological experiments on populations of neurons where the concentration of carbachol can be varied. Indeed, the increase (decrease) of carbachol can be interpreted as effectively reducing (increasing) the strength of SFA. As a matter of fact, the increase of the adaptation strength leads to shorter (longer) Up (Down) state durations somehow mimicking the effect of charbachol in in vitro experiments, where spontaneous slow waves are observed. Furthermore, the scenario depicted in [1], where an increase of the concentration of carbachol induces a transition from anesthesia-like to sleep-like dynamics is consistent with our results based on the variation of the adaptation strength.
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BibTeX
@article{martelloni2026slow,
title = {{Slow relaxation oscillations in multi-scale adaptive next generation neural masses}},
author = {Gianluca Martelloni and David Angulo-Garcia and Giacomo Innocenti and Alessandro Torcini and Simona Olmi},
journal = {Physica D: Nonlinear Phenomena},
year = {2026},
month = oct,
doi = {10.1016/j.physd.2026.135451},
url = {https://hal.science/hal-05805173v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Slow relaxation oscillations in multi-scale adaptive next generation neural masses
AU - Gianluca Martelloni
AU - David Angulo-Garcia
AU - Giacomo Innocenti
AU - Alessandro Torcini
AU - Simona Olmi
PY - 2026
DA - 2026/10/19
JO - Physica D: Nonlinear Phenomena
DO - 10.1016/j.physd.2026.135451
UR - https://hal.science/hal-05805173v1
AB - We have studied the mean field dynamics of heterogenous quadratic integrate-and-fire neurons in presence of spike frequency adaptation (SFA) by considering the exact formulation in terms of the next generation neural mass models (NG-NMMs). In particular, we have examined the emergence of slow relaxation oscillations in purely excitatory and excitatory-inhibitory NG-NMMs with SFA acting only on the excitatory population. Relaxation oscillations (ROs) connect low firing state (Down state) to high firing state (Up state) via the slow adaptation. In the examined cases, the orbit relaxes towards the Up State via a sequence of collective damped oscillations (peaks of activity), thus revealing population bursting dynamics. The slower is the adaptation time scale (the lower is the adaptation strength) the higher is the complexity (number of peaks) displayed by the relaxation oscillations. The increase in the number of peaks is due to spike-adding sequences controlled by the SFA parameters. The increase in the adaptation time scale leads to a chaos-induced spike-adding mechanism where the spike-adding occurs via intermediate chaotic transition regions. Quite peculiarly these chaotic regimes can be of two different types: Population Spiking and Population Bursting Chaos. The emergence of ROs with an increasing number of peaks, controlled by the adaptation strength, occurs via a different spike-adding mechanism. The ROs with (n + 1) peaks emerge through a saddle-node bifurcation, while coexisting, in a very narrow parameter region, with the solutions with n peaks, that looses stability via a sub-critical period doubling transition. In this case chaotic dynamics is not observable at the spike-adding bifurcations, but only in proximity of the population spiking-bursting transition. The considered NG-NMMs with SFA could be employed to interpret the results of neuro-physiological experiments on populations of neurons where the concentration of carbachol can be varied. Indeed, the increase (decrease) of carbachol can be interpreted as effectively reducing (increasing) the strength of SFA. As a matter of fact, the increase of the adaptation strength leads to shorter (longer) Up (Down) state durations somehow mimicking the effect of charbachol in in vitro experiments, where spontaneous slow waves are observed. Furthermore, the scenario depicted in [1], where an increase of the concentration of carbachol induces a transition from anesthesia-like to sleep-like dynamics is consistent with our results based on the variation of the adaptation strength.
SN - 0167-2789
SN - 1872-8022
ER -