Clustering in Inhibitory Neural Networks with Nearest Neighbor Coupling

Miller, Jennifer M.; Ryu, Hwayeon; Teymuroglu, Zeynep; Booth, Victoria; Campbell, Sue Ann

doi:10.1007/978-1-4939-2782-1_5

Cited by 9 publications

(20 citation statements)

References 25 publications

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“…He showed that these results gave a good prediction of stability for a variety of model networks. Recently, similar results have been obtained for networks with nearest-neighbour coupling [21]. Phase model analysis has been extensively used to study phase-locking in pairs of model and experimental neurons [12,22,19].…”

Section: Introductionsupporting

confidence: 64%

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Phase models and clustering in networks of oscillators with delayed coupling

Campbell

Wang

2018

Physica D: Nonlinear Phenomena

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We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to study the existence and stability of cluster solutions. Cluster solutions are phase locked solutions where the oscillators separate into groups. Oscillators within a group are synchronized while those in different groups are phase-locked. We give model independent existence and stability results for symmetric cluster solutions. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies.

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Section: Introductionsupporting

confidence: 64%

“…Theorem 6. For a network with a circulant connectivity matrix, the system (10) admits solutions of the form (20) and (21) if N = 4p for some integer p, and p−1 k=0 w 4k+1 = p−1 k=0 w 4k+3 .…”

Section: Other Types Of Cluster Solutionsmentioning

confidence: 99%

Phase models and clustering in networks of oscillators with delayed coupling

Campbell

Wang

2018

Physica D: Nonlinear Phenomena

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“…Thus we conclude that the 1-cluster (totally synchronized) solution always exists. This is consistent with results for systems with first and second nearest neighbour coupling [31]. To proceed further, take the difference of equations 22 Repeating this with other pairs of equations leads to the same constraint on ψ m and the conditions (21).…”

Section: The Second Case: K Th Neighbor Coupling With Additional Coupsupporting

confidence: 73%

Spatially localized cluster solutions in inhibitory neural networks

Ryu

Miller

Teymuroglu

et al. 2020

Preprint

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Neurons in the inhibitory network of the striatum display cell assembly firing patterns which recent results suggest may consist of spatially compact neural clusters. Previous computational modeling of striatal neural networks has indicated that non-monotonic, distance-dependent coupling may promote spatially localized cluster firing. Here, we identify conditions for the existence and stability of cluster firing solutions in which clusters consist of spatially adjacent neurons in inhibitory neural networks. We consider simple non-monotonic, distance-dependent connectivity schemes in weakly coupled 1-D networks where cells make strong connections with their kth nearest neighbors on each side. Using the phase model reduction of the network system, we prove the existence of cluster solutions where neurons that are spatially close together are also synchronized in the same cluster, and find stability conditions for these solutions. Our analysis predicts the long-term behavior for networks of neurons, and we confirm our results by numerical simulations of biophysical neuron network models. Additionally, we add weaker coupling between closer neighbors as a perturbation to our network connectivity. We analyze the existence and stability of cluster solutions of the perturbed network and validate our results with numerical simulations. Our results demonstrate that an inhibitory network with non-monotonic, distance-dependent connectivity can exhibit cluster solutions where adjacent cells fire together.

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“…In neural network models, the formation of neural assemblies has been analyzed by identifying cluster solutions in networks of intrinsically oscillating neurons [16,17,28,15,22,31,7]. Clustering defines a type of solution where the network of oscillators breaks into subgroups.…”

Section: Introductionmentioning

confidence: 99%

“…In previous work [31,7], we used the phase model approach to determine existence and stability conditions of cluster solutions of networks with neurons arranged in a 1-dimensional ring, of arbitrary size, with various connectivity schemes. As in many other studies [5,33], our work focused on cluster solutions where the phase difference between any two adjacent neurons in the network is the same.…”

Section: Introductionmentioning

confidence: 99%

Spatially localized cluster solutions in inhibitory neural networks

Ryu

Miller

Teymuroglu

et al. 2021

Mathematical Biosciences

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Neurons in the inhibitory network of the striatum display cell assembly firing patterns which recent results suggest may consist of spatially compact neural clusters. Previous computational modeling of striatal neural networks has indicated that non-monotonic, distance-dependent coupling may promote spatially localized cluster firing. Here, we identify conditions for the existence and stability of cluster firing solutions in which clusters consist of spatially adjacent neurons in inhibitory neural networks. We consider simple non-monotonic, distance-dependent connectivity schemes in weakly coupled 1-D networks where cells make strong connections with their k th nearest neighbors on each side. Using the phase model reduction of the network system, we prove the existence of cluster solutions where neurons that are spatially close together are also synchronized in the same cluster, and find stability conditions for these solutions. Our analysis predicts the long-term behavior for networks of neurons, and we confirm our results by numerical simulations of biophysical neuron network models. Additionally, we add weaker coupling between closer neighbors as a perturbation to our network connectivity. We analyze the existence and stability of cluster solutions of the perturbed network and validate our results with numerical simulations. Our results demonstrate that an inhibitory network with non-monotonic, distance-dependent connectivity can exhibit cluster

show abstract

Clustering in Inhibitory Neural Networks with Nearest Neighbor Coupling

Cited by 9 publications

References 25 publications

Phase models and clustering in networks of oscillators with delayed coupling

Phase models and clustering in networks of oscillators with delayed coupling

Spatially localized cluster solutions in inhibitory neural networks

Spatially localized cluster solutions in inhibitory neural networks

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