Multiple-timescale dynamics, mixed mode oscillations and mixed affective states in a model of Bipolar Disorder DOI Creative Commons
Efstathios Pavlidis, Fabien Campillo, Albert Goldbeter

et al.

bioRxiv (Cold Spring Harbor Laboratory), Journal Year: 2022, Volume and Issue: unknown

Published: March 25, 2022

Abstract Mixed affective states in bipolar disorder (BD) is a common psychiatric condition that occurs when symptoms of the two opposite poles coexist during an episode mania or depression. A four-dimensional model by A. Goldbeter [27, 28] rests upon notion manic and depressive are produced competing auto-inhibited neural networks. Some rich dynamics this can produce, include complex rhythms formed both small-amplitude (subthreshold) large-amplitude (suprathreshold) oscillations could correspond to mixed states. These commonly referred as mode (MMOs) they have already been studied many different contexts [7, 50]. In order accurately explain these one has apply mathematical apparatus makes full use timescale separation between variables. Here we framework multiple-timescale BD understand mechanisms underpinning observed changing mood. We show be understood MMOs due so-called folded-node singularity . Moreover, explore bifurcation structure system provide possible biological interpretations our findings. Finally, robustness regime stochastic noise propose minimal three-dimensional which, with addition noise, exhibits similar yet purely noise-driven dynamics. The broader significance work introduce tools used analyse potentially control future, more biologically grounded models BD.

Language: Английский

A geometric analysis of the SIR, SIRS and SIRWS epidemiological models DOI
Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Andrea Pugliese

et al.

Nonlinear Analysis Real World Applications, Journal Year: 2020, Volume and Issue: 58, P. 103220 - 103220

Published: Sept. 28, 2020

Language: Английский

Citations

57
Bursting in a next generation neural mass model with synaptic dynamics: a slow–fast approach DOI Creative Commons
Halgurd Taher, Daniele Avitabile, Mathieu Desroches

et al.

Nonlinear Dynamics, Journal Year: 2022, Volume and Issue: 108(4), P. 4261 - 4285

Published: April 19, 2022

Abstract We report a detailed analysis on the emergence of bursting in recently developed neural mass model that includes short-term synaptic plasticity. Neural models can mimic collective dynamics large-scale neuronal populations terms few macroscopic variables like mean membrane potential and firing rate. The present one is particularly important, as it represents an exact meanfield limit synaptically coupled quadratic integrate fire (QIF) neurons. Without dynamics, periodic external current with slow frequency $$\varepsilon $$ ε lead to burst-like dynamics. patterns be understood using singular perturbation theory, specifically slow–fast dissection. With timescale separation leads variety phenomena their role for becomes inordinately more intricate. Canards are crucial understand route bursting. They describe trajectories evolving nearby repelling locally invariant sets system exist at transition between subthreshold Near = 0$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">ε=0 , we peculiar jump-on canards which block continuous In biologically plausible -regime, this bursts emerge via consecutive spike-adding transitions. onset complex involves mixed-type-like torus form very first spikes burst follow fast-subsystem cycles. numerically evidence same mechanisms responsible QIF network plastic synapses. main conclusions apply network, owing exactness limit.

Language: Английский

Citations

29
Compound bursting behaviors in a forced Mathieu-van der Pol-Duffing system DOI
Xindong Ma,

Daixian Xia,

Wen‐An Jiang

et al.

Chaos Solitons & Fractals, Journal Year: 2021, Volume and Issue: 147, P. 110967 - 110967

Published: April 24, 2021

Language: Английский

Citations

28
Classification of bursting patterns: A tale of two ducks DOI Creative Commons
Mathieu Desroches, John Rinzel, Serafim Rodrigues

et al.

PLoS Computational Biology, Journal Year: 2022, Volume and Issue: 18(2), P. e1009752 - e1009752

Published: Feb. 24, 2022

Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic intense research computational biology for several decades. The classification bursting oscillations systems subject active since early 1980s and still ongoing. As by-product, it establishes analytical numerical foundations studying complex temporal behaviors multiple timescale models cellular activity. In this review, we first present seminal works Rinzel Izhikevich classifying patterns systems. We recall complementary mathematical approach by Bertram colleagues, then Golubitsky which, together with Rinzel-Izhikevich proposals, provide state-of-the-art these classifications. Beyond classical approaches, review recent example falls outside previous Generalizing leads us propose an extended classification, which requires analysis both fast slow subsystems underlying slow-fast model allows dissection larger class bursters. Namely, general framework subthreshold superthreshold oscillations. A new bursters at least 2 variables added, denote folded-node bursters, convey idea bursts are initiated annihilated via singularity. Key mechanism so-called canard duck orbits, organizing underpinning excitability structure. describe main families depending upon phase (active/spiking silent/nonspiking) cycle during dynamics occurs. classify give examples minimal displaying novel patterns. Finally, biophysical reinterpreting generic conductance-based episodic burster as burster, showing associated explain its over parameter region than subsystem approach.

Language: Английский

Citations

17
Neural mass modeling of slow-fast dynamics of seizure initiation and abortion DOI Creative Commons
Elif Köksal Ersöz, Julien Modolo, Fabrice Bartoloméi

et al.

PLoS Computational Biology, Journal Year: 2020, Volume and Issue: 16(11), P. e1008430 - e1008430

Published: Nov. 9, 2020

Epilepsy is a dynamic and complex neurological disease affecting about 1% of the worldwide population, among which 30% patients are drug-resistant. characterized by recurrent episodes paroxysmal neural discharges (the so-called seizures), manifest themselves through large-amplitude rhythmic activity observed in depth-EEG recordings, particular local field potentials (LFPs). The signature characterizing transition to seizures involves oscillatory patterns, could serve as marker prevent seizure initiation triggering appropriate therapeutic neurostimulation methods. To investigate such protocols, neurophysiological lumped-parameter models at mesoscopic scale, namely mass models, powerful tools that not only mimic LFP signals but also give insights on mechanisms related different stages seizures. Here, we analyze multiple time-scale dynamics model explain underlying structure oscillations before initiation. We population-specific effects stimulation dependence parameters synaptic timescales. In particular, show intermediate frequencies (>20 Hz) can abort if timescale difference pronounced. Those results have potential design brain protocols based properties tissue.

Language: Английский

Citations

21
Long-living transients in ecological models: recent progress, new challenges, and open questions DOI Creative Commons
Andrew Morozov, Ulrike Feudel, Alan Hastings

et al.

Physics of Life Reviews, Journal Year: 2024, Volume and Issue: 51, P. 423 - 441

Published: Nov. 13, 2024

Traditionally, mathematical models in ecology placed an emphasis on asymptotic, long-term dynamics. However, a large number of recent studies highlighted the importance transient dynamics ecological and eco-evolutionary systems, particular 'long transients' that can last for hundreds generations or even longer. Many as well empirical indicated system function long time certain state regime (a 'metastable regime') but later exhibits abrupt transition to another not preceded by any parameter change (or following occurred before transition). This scenario where tipping occurs without apparent source shift is also referred 'metastability'. Despite considerable evidence presence transients real-world systems models, until recently research into long-living has remained its infancy, largely lacking systematisation. Within past decade, however, substantial progress been made creating unifying theory deterministic stochastic systems. considerably accelerated further transients, those characterised more complicated patterns and/or underlying mechanisms. The main goal this review provide overview related shifts We pay special attention role environmental stochasticity, effect multiple timescales (slow-fast systems), spatial patterns, relation between synchronisation. discuss current challenges open questions understanding with applications ecosystems

Language: Английский

Citations

2
Route to mixed-mode oscillations via step-shaped sharp transition of equilibria in a nonlinear gyroscope oscillator DOI
Mengke Wei, Xiujing Han, Qinsheng Bi

et al.

Communications in Nonlinear Science and Numerical Simulation, Journal Year: 2023, Volume and Issue: 127, P. 107545 - 107545

Published: Sept. 16, 2023

Language: Английский

Citations

3
Canard solutions in neural mass models: consequences on critical regimes DOI Creative Commons
Elif Köksal Ersöz, Fabrice Wendling

The Journal of Mathematical Neuroscience, Journal Year: 2021, Volume and Issue: 11(1)

Published: Sept. 16, 2021

Abstract Mathematical models at multiple temporal and spatial scales can unveil the fundamental mechanisms of critical transitions in brain activities. Neural mass (NMMs) consider average dynamics interconnected neuronal subpopulations without explicitly representing underlying cellular activity. The mesoscopic level offered by neural formulation has been used to model electroencephalographic (EEG) recordings investigate various cerebral mechanisms, such as generation physiological pathological In this work, we a NMM widely accepted context epilepsy, which includes four interacting with different synaptic kinetics. Due resulting three-time-scale structure, yields complex oscillations relaxation bursting types. By applying principles geometric singular perturbation theory, existence canard solutions detail how they organize excitability properties model. particular, show that boundaries between epileptic discharges background activity are determined solutions. Finally report canard-mediated small-amplitude frequency-specific simulated local field potentials for decreased inhibition conditions. Interestingly, actually observed intracerebral EEG signals recorded patients during pre-ictal periods, close seizure onsets.

Language: Английский

Citations

6
Multiple-timescale dynamics, mixed mode oscillations and mixed affective states in a model of bipolar disorder DOI
Efstathios Pavlidis, Fabien Campillo, Albert Goldbeter

et al.

Cognitive Neurodynamics, Journal Year: 2022, Volume and Issue: 18(6), P. 3239 - 3257

Published: Oct. 26, 2022

Language: Английский

Citations

3
Canard Mechanism and Rhythm Dynamics of Neuron Models DOI Creative Commons
Feibiao Zhan,

Yingteng Zhang,

Jian Song

et al.

Mathematics, Journal Year: 2023, Volume and Issue: 11(13), P. 2874 - 2874

Published: June 27, 2023

Canards are a type of transient dynamics that occur in singularly perturbed systems, and they specific types solutions with varied dynamic behaviours at the boundary region. This paper introduces emergence development canard phenomena neuron model. The singular perturbation system general model is investigated, link between transition from to summarised. First, relationship folded saddle-type parabolic burster, as well firing-threshold manifold, established. Moreover, association mixed-mode oscillation node unique. Furthermore, connection limit-cycle (singular Hopf bifurcation) stated. In addition, torus tonic spiking bursting illustrated. Finally, manifestations these demonstrated, such bifurcation, folded-node canard, “blue sky catastrophe”. summary outlook this point realistic possibility canards, which have not yet been discovered

Language: Английский

Citations

1