Observable for a Large System of Globally Coupled Excitable Units

Boari, Santiago; Uribarri, Gonzalo; Amador, Ana; Mindlin, Gabriel B.

doi:10.3390/mca24020037

Cited by 4 publications

(4 citation statements)

References 36 publications

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“…The method, related to the so-called Ott-Antonsen ansatz [35][36][37][38][39][40][41], allows to obtain exact, low-dimensional firing rate equations for ensembles of QIF neurons, see also [42][43][44]. The FRE for QIF neurons have been used to investigate numerous problems regarding the dynamics of networks of chemically coupled QIF neurons [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64]. Remarkably, previous work has also sought to apply this approach to networks with both chemical and electrical coupling [65].…”

Section: Introductionmentioning

confidence: 99%

Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks

et al. 2019

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Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect is less understood. This limitation is further magnified by the impossibility of traditional neuronal mean-field models -also known as firing rate models, or firing rate equations-to account for electrical synapses. Here we introduce a novel firing rate model that exactly describes the mean field dynamics of heterogeneous populations of quadratic integrate-and-fire (QIF) neurons with both chemical and electrical synapses. The mathematical analysis of the firing rate model reveals a well-established bifurcation scenario for networks with chemical synapses, characterized by a codimension-2 Cusp point and persistent states for strong recurrent excitatory coupling. The inclusion of electrical coupling generally implies neuronal synchrony by virtue of a supercritical Hopf bifurcation. This transforms the Cusp scenario into a bifurcation scenario characterized by three codimension-2 points (Cusp, Takens-Bogdanov, and Saddle-Node Separatrix Loop), which greatly reduces the possibility for persistent states. This is generic for heterogeneous QIF networks with both chemical and electrical coupling. Our results agree with several numerical studies on the dynamics of large networks of heterogeneous spiking neurons with electrical and chemical coupling.

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Section: Introductionmentioning

confidence: 99%

Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks

et al. 2019

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“…We then extracted and analysed the features of LFP elicited by the auditory presentation of BOS and found that it has signatures of the oscillatory properties of the behaviour in terms of pronounced and consistent minima. Previous works have suggested that this would require the overlap of synaptic currents from many neurons to display a significant trait distinguishable from noise (Boari et al, 2019; Buzsaki et al, 2012). We found that the occurrence of these minima was related to the syllabic repetition rates and that on multiple recording sites they were consistent in timing within song phrases and preserved across individuals.…”

Section: Discussionmentioning

confidence: 99%

Neural oscillations are locked to birdsong rhythms in canaries

Boari

Mindlin

Amador

2022

Eur J of Neuroscience

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How vocal communication signals are represented in the cortex is a major challenge for behavioural neuroscience. Beyond a descriptive code, it is relevant to unveil the dynamical mechanism responsible for the neural representation of auditory stimuli. In this work, we report evidence of synchronous neural activity in nucleus HVC, a telencephalic area of canaries (Serinus canaria), in response to auditory playback of the bird's own song. The rhythmic features of canary song allowed us to show that this large‐scale synchronization was locked to defined features of the behaviour. We recorded neural activity in a brain region where sensorimotor integration occurs, showing the presence of well‐defined oscillations in the local field potentials, which are locked to song rhythm. We also show a correspondence between local field potentials, multiunit activity and single unit activity within the same brain region. Overall, our results show that the rhythmic features of the vocal behaviour are represented in a telencephalic region of canaries.

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“…In computational neuroscience, both exponential 28 and αpulses 29,30 are typically studied. The former ones are simpler to handle, as they require one variable per neuron per field type…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Collective dynamics in the presence of finite-width pulses

Afifurrahman

Ullner

Politi

2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The idealization of neuronal pulses as δ-spikes is a convenient approach in neuroscience but can sometimes lead to erroneous conclusions. We investigate the effect of a finite pulse width on the dynamics of balanced neuronal networks. In particular, we study two populations of identical excitatory and inhibitory neurons in a random network of phase oscillators coupled through exponential pulses with different widths. We consider three coupling functions inspired by leaky integrate-and-fire neurons with delay and type I phase-response curves. By exploring the role of the pulse widths for different coupling strengths, we find a robust collective irregular dynamics, which collapses onto a fully synchronous regime if the inhibitory pulses are sufficiently wider than the excitatory ones. The transition to synchrony is accompanied by hysteretic phenomena (i.e., the co-existence of collective irregular and synchronous dynamics). Our numerical results are supported by a detailed scaling and stability analysis of the fully synchronous solution. A conjectured first-order phase transition emerging for δ-spikes is smoothed out for finite-width pulses.

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Observable for a Large System of Globally Coupled Excitable Units

Cited by 4 publications

References 36 publications

Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks

Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks

Neural oscillations are locked to birdsong rhythms in canaries

Collective dynamics in the presence of finite-width pulses

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