Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks
We study a model for a network of synaptically coupled, excitable neurons to identify the role of coupling delays in generating different network behaviors. The network consists of two distinct populations, each of which contains one excitatory-inhibitory neuron pair. The two pairs are coupled via d...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2020403?viewType=HTML |
| _version_ | 1819113435649015808 |
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| author | Hwayeon Ryu Sue Ann Campbell |
| author_facet | Hwayeon Ryu Sue Ann Campbell |
| author_sort | Hwayeon Ryu |
| collection | DOAJ |
| description | We study a model for a network of synaptically coupled, excitable neurons to identify the role of coupling delays in generating different network behaviors. The network consists of two distinct populations, each of which contains one excitatory-inhibitory neuron pair. The two pairs are coupled via delayed synaptic coupling between the excitatory neurons, while each inhibitory neuron is connected only to the corresponding excitatory neuron in the same population. We show that multiple equilibria can exist depending on the strength of the excitatory coupling between the populations. We conduct linear stability analysis of the equilibria and derive necessary conditions for delay-induced Hopf bifurcation. We show that these can induce two qualitatively different phase-locked behaviors, with the type of behavior determined by the sizes of the coupling delays. Numerical bifurcation analysis and simulations supplement and confirm our analytical results. Our work shows that the resting equilibrium point is unaffected by the coupling, thus the network exhibits bistability between a rest state and an oscillatory state. This may help understand how rhythms spontaneously arise in neuronal networks. |
| first_indexed | 2024-12-22T04:29:22Z |
| format | Article |
| id | doaj.art-58b98b8606814949be8362d7571a340f |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-22T04:29:22Z |
| publishDate | 2020-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-58b98b8606814949be8362d7571a340f2022-12-21T18:39:04ZengAIMS PressMathematical Biosciences and Engineering1551-00182020-11-011767931795710.3934/mbe.2020403Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networksHwayeon Ryu 0Sue Ann Campbell 11. Department of Mathematics and Statistics, Elon University, 50 Campus Drive, Elon, NC 27244, USA2. Department of Applied Mathematics and Centre for Theoretical Neuroscience, University of Waterloo, Waterloo, Ontario, N2L 3G1, CanadaWe study a model for a network of synaptically coupled, excitable neurons to identify the role of coupling delays in generating different network behaviors. The network consists of two distinct populations, each of which contains one excitatory-inhibitory neuron pair. The two pairs are coupled via delayed synaptic coupling between the excitatory neurons, while each inhibitory neuron is connected only to the corresponding excitatory neuron in the same population. We show that multiple equilibria can exist depending on the strength of the excitatory coupling between the populations. We conduct linear stability analysis of the equilibria and derive necessary conditions for delay-induced Hopf bifurcation. We show that these can induce two qualitatively different phase-locked behaviors, with the type of behavior determined by the sizes of the coupling delays. Numerical bifurcation analysis and simulations supplement and confirm our analytical results. Our work shows that the resting equilibrium point is unaffected by the coupling, thus the network exhibits bistability between a rest state and an oscillatory state. This may help understand how rhythms spontaneously arise in neuronal networks.https://www.aimspress.com/article/doi/10.3934/mbe.2020403?viewType=HTMLneural networksphase-lockingcoupling delayshopf bifurcation |
| spellingShingle | Hwayeon Ryu Sue Ann Campbell Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks Mathematical Biosciences and Engineering neural networks phase-locking coupling delays hopf bifurcation |
| title | Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks |
| title_full | Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks |
| title_fullStr | Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks |
| title_full_unstemmed | Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks |
| title_short | Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks |
| title_sort | stability bifurcation and phase locking of time delayed excitatory inhibitory neural networks |
| topic | neural networks phase-locking coupling delays hopf bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2020403?viewType=HTML |
| work_keys_str_mv | AT hwayeonryu stabilitybifurcationandphaselockingoftimedelayedexcitatoryinhibitoryneuralnetworks AT sueanncampbell stabilitybifurcationandphaselockingoftimedelayedexcitatoryinhibitoryneuralnetworks |