Dynamics and bifurcations in multistable 3-cell neural networks

Collens, Jarod; Pusuluri, Krishna; Kelley, Aaron; Knapper, Drake E.; Xing, Tingli; Basodi, Sunitha; Alaçam, Deniz; Shilnikov, Andrey

doi:10.1063/5.0011374

Cited by 13 publications

(7 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such fast synapses happened to be useful for understanding synchronized neuronal activity, including bursting with inhibitory synapses, and multistability in small, weekly coupled neural networks [59][60][61][62][63][64][65][66][67] . Moreover, this assumption has the benefit of simplifying the network dynamics, facilitating both analysis and simulation [68][69][70] .…”

Section: Modeling Synaptic Dynamics: From Fast To Slowmentioning

confidence: 99%

Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits

Scully

Bourahmah

Bloom

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

The purpose of this paper is to serve as an instructive resource and a reference catalog for biologically plausible modeling with i) conductance-based models, coupled with ii) strength varying slow synapse models, culminating in iii) two canonical pair-wise rhythm-generating networks. We document the properties of basic network components: cell models and synaptic models, which are prerequisites for proper network assembly. Using the slow-fast decomposition we present a detailed analysis of the cellular dynamics including a discussion of the most relevant bifurcations. Several approaches to model synaptic coupling are also discussed, and a new logistic model of slow synapses is introduced. Finally, we describe and examine two types of bicellular rhythm-generating networks: i) half center oscillators ii) excitatory-inhibitory pairs and elucidate a key principle - the network hysteresis underlying the stable onset of emergent slow bursting in these neural building blocks. These two cell networks are a basis for more complicated neural circuits of rhythmogenesis and feature in our models of swim central pattern generators.

show abstract

Section: Modeling Synaptic Dynamics: From Fast To Slowmentioning

confidence: 99%

Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits

Scully

Bourahmah

Bloom

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Such fast synapses happened to be useful for understanding synchronized neuronal activity, including bursting with inhibitory synapses, and multistability in small, weekly coupled neural networks [61][62][63][64][65][66][67][68][69]. Moreover, this assumption has the benefit of simplifying the network dynamics, facilitating both analysis and simulation [70][71][72].…”

Section: Synapse Typesmentioning

confidence: 99%

Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits

Scully

Bourahmah

Bloom

et al. 2022

Preprint

View full text Add to dashboard Cite

The purpose of this paper is trifold -- to serve as an instructive resource and a reference catalog for biologically plausible modeling with i) conductance-based models, coupled with ii) strength-varying slow synapse models, culminating in iii) two canonical pair-wise rhythm-generating networks. We document the properties of basic network components: cell models and synaptic models, which are prerequisites for proper network assembly. Using the slow-fast decomposition we present a detailed analysis of the cellular dynamics including a discussion of the most relevant bifurcations. Several approaches to model synaptic coupling are also discussed, and a new logistic model of slow synapses is introduced. Finally, we describe and examine two types of bicellular rhythm-generating networks: i) half-center oscillators ii) excitatory-inhibitory pairs and elucidate a key principle -- the network hysteresis underlying the stable onset of emergent slow bursting in these neural building blocks. These two cell networks are a basis for more complicated neural circuits of rhythmogenesis and feature in our models of swim central pattern generators.

show abstract

“…p is the number of neighbors connected on each side except for its two closest ones. The sigmoidal nonlinear function Γ (x j ) is used to model the chemical synaptic dynamics [35,36]:…”

Section: Neuronal Networkmentioning

confidence: 99%

Chimera states in a neuronal network under the action of an electric field

Simo,

Njougouo,

Aristides

et al. 2021

Preprint

View full text Add to dashboard Cite

The phenomenon of the chimera state symbolizes the coexistence of coherent and incoherent sections of a given population. This phenomenon identified in several physical and biological systems presents several variants, including the multichimera states and the traveling chimera state. Here, we numerically study the influence of a weak external electric field on the dynamics of a network of Hindmarsh-Rose (HR) neurons coupled locally by an electrical interaction and nonlocally by a chemical one. We first focus on the phenomena of traveling chimera states and multicluster oscillating breathers that appear in the electric field's absence. Then in the field's presence, we highlight the presence of a chimera state, a multichimera state, an alternating chimera state and a multicluster traveling chimera.

show abstract

Dynamics and bifurcations in multistable 3-cell neural networks

Cited by 13 publications

References 56 publications

Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits

Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits

Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits

Chimera states in a neuronal network under the action of an electric field

Contact Info

Product

Resources

About