Periodic Solutions in Threshold-Linear Networks and Their Entrainment

Bel, Andrea; Cobiaga, Romina; Reartes, Walter; Rotstein, Horacio G.

doi:10.1137/20m1337831

Cited by 11 publications

(4 citation statements)

References 24 publications

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“…In this work, we have used the odd cycle rule to study oscillations in BG. However, oscillatory dynamics and the odd cycle rule show up in many chemical, biological and even social systems such as neuronal networks Bel et al, 2021 , psychological networks Greenwald et al, 2002 , social and political networks Leskovec et al, 2010 ; Milo et al, 2004 ; Heider, 1946 ; Cartwright and Harary, 1956 , resting-state networks in autism Moradimanesh et al, 2021 and gene networks Farcot and Gouzé, 2010 ; Allahyari et al, 2022 . In fact, originally Thomas’ conjecture Thomas, 1980 about the structural conditions for oscillations was made for gene regulatory networks.…”

Section: Discussionmentioning

confidence: 99%

Structural constraints on the emergence of oscillations in multi-population neural networks

Zang,

Liu,

Helson

et al. 2024

eLife

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Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Therefore, it is important to determine the causes of oscillations in a network. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons. Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.

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Section: Discussionmentioning

confidence: 99%

Structural constraints on the emergence of oscillations in multi-population neural networks

Zang,

Liu,

Helson

et al. 2024

eLife

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“…It is, nonetheless, nontrivial to prove that the limit cycle shown in Figure 5 exists. A recent proof was given for a special family of TLNs constructed from any k-cycle graph [BCRR21].…”

Section: Tlns and Hyperplane Arrangementsmentioning

confidence: 99%

Graph rules for recurrent neural network dynamics: extended version

Curto¹,

Morrison²

2023

Preprint

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“…In this work we have used the odd cycle rule to study oscillations in basal ganglia. However, oscillatory dynamics and the odd cycle rule show up in many chemical, biological and even social systems such as neuronal networks [40], psychological networks [41], social and political networks [42,43,44,45], resting-state networks in autism [46] and gene networks [47,48].…”

Section: Beyond Neural Networkmentioning

confidence: 99%

Structural constraints on the emergence of oscillations in multi-population neural networks

Zang¹,

Liu²,

Helson³

et al. 2023

Preprint

View full text Add to dashboard Cite

Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Therefore, it is important to determine the causes of oscillations in a network.Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons.Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.

show abstract

Periodic Solutions in Threshold-Linear Networks and Their Entrainment

Cited by 11 publications

References 24 publications

Structural constraints on the emergence of oscillations in multi-population neural networks

Structural constraints on the emergence of oscillations in multi-population neural networks

Graph rules for recurrent neural network dynamics: extended version

Structural constraints on the emergence of oscillations in multi-population neural networks

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