Irregular behavior in an excitatory-inhibitory neuronal network

Park, Choongseok; Terman, David

doi:10.1063/1.3430545

Cited by 6 publications

(5 citation statements)

References 17 publications

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“…example, one of the consequences of this result is that an activation function with strong variations produces chaos in the network provided the internal decay of the neurons is small. This conclusion is of a different nature to some recent results in this direction; see, e.g., [4,36], where the authors consider excitatory-inhibitory networks and find conditions for when this model exhibits irregular and chaotic-like solutions.…”

Section: Discussioncontrasting

confidence: 74%

Global dynamics of discrete neural networks allowing non-monotonic activation functions

Liz

Ruiz-Herrera

2014

Nonlinearity

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We show that in discrete models of Hopfield type some properties of global stability and chaotic behaviour are coded in the dynamics of a related onedimensional equation. Using this fact, we obtain some new results on stability and chaos for a system of delayed neural networks; some relevant properties of our results are that we do not require monotonicity properties in the activation function, we allow any architecture of the network, and the conclusions are independent of the size of the time delays.

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Section: Discussioncontrasting

confidence: 74%

Global dynamics of discrete neural networks allowing non-monotonic activation functions

Liz

Ruiz-Herrera

2014

Nonlinearity

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“…However, in realistic neural systems, the excitatory and inhibitory neurons are coexisting [21]. Such excitatory-inhibitory (E-I) networks arise in many regions throughout the central nervous system and display complex patterns of activity [22,24]. The behavior of E-I networks is critical for understanding how neural circuits produce cognitive function [23].…”

Section: Introductionmentioning

confidence: 99%

How to enhance the dynamic range of excitatory-inhibitory excitable networks

et al. 2012

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We investigate the collective dynamics of excitatory-inhibitory excitable networks in response to external stimuli. How to enhance the dynamic range, which represents the ability of networks to encode external stimuli, is crucial to many applications. We regard the system as a two-layer network (E layer and I layer) and explore the criticality and dynamic range on diverse networks. Interestingly, we find that phase transition occurs when the dominant eigenvalue of the E layer's weighted adjacency matrix is exactly 1, which is only determined by the topology of the E layer. Meanwhile, it is shown that the dynamic range is maximized at a critical state. Based on theoretical analysis, we propose an inhibitory factor for each excitatory node. We suggest that if nodes with high inhibitory factors are cut out from the I layer, the dynamic range could be further enhanced. However, because of the sparseness of networks and passive function of inhibitory nodes, the improvement is relatively small compared to the original dynamic range. Even so, this provides a strategy to enhance the dynamic range.

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“…A study of the relationship between patterns in the GPi and STN and their modification after the introduction of a dopamine agonist such as apomorphine might possibly shed light on the mathematical properties of the connection between them, which has been proposed to contribute to the generation of irregular spiking in the basal ganglia. 69 In other recent work by our group we have found similarities between the GPi discharge in PD and the behavior of turbulent fluids. 17 This result is in agreement with the present finding, since turbulent systems exhibit positive Lyapunov exponents.…”

Section: Discussionmentioning

confidence: 52%

Finite Dimensional Structure of the Gpi Discharge in Patients With Parkinson's Disease

Andres

Cerquetti

Merello

2011

Int. J. Neur. Syst.

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Stochastic systems are infinitely dimensional and deterministic systems are low dimensional, while real systems lie somewhere between these two limit cases. If the calculation of a low (finite) dimension is in fact possible, one could conclude that the system under study is not purely random. In the present work we calculate the maximal Lyapunov exponent from interspike intervals time series recorded from the internal segment of the Globus Pallidusfrom patients with Parkinson's disease. We show the convergence of the maximal Lyapunov exponent at a dimension equal to 7 or 8, which is therefore our estimation of the embedding dimension for the system. For dimensions below 7 the observed behavior is what would be expected from a stochastic system or a complex system projecting onto lower dimensional spaces. The maximal Lyapunov exponent did not show any differences between tremor and akineto-rigid forms of the disease. However, it did decay with the value of motor Unified Parkinson's Disease Rating Scale -OFF scores. Patients with a more severe disease (higher UPDRS-OFF score) showed a lower value of the maximal Lyapunov exponent. Taken together, both indexes (the maximal Lyapunov exponent and the embedding dimension) remark the importance of taking into consideration the system's non-linear properties for a better understanding of the information transmission in the basal ganglia.

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Irregular behavior in an excitatory-inhibitory neuronal network

Cited by 6 publications

References 17 publications

Global dynamics of discrete neural networks allowing non-monotonic activation functions

Global dynamics of discrete neural networks allowing non-monotonic activation functions

How to enhance the dynamic range of excitatory-inhibitory excitable networks

Finite Dimensional Structure of the Gpi Discharge in Patients With Parkinson's Disease

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