Delays in activity-based neural networks

In this paper, we study the effect of two distinct discrete delays on the dynamics of a Wilson–Cowan neural network. This activity-based model describes the dynamics of synaptically interacting excitatory and inhibitory neuronal populations. We discuss the interpretation of the delays in the language of neurobiology and show how they can contribute to the generation of network rhythms. First, we focus on the use of linear stability theory to show how to destabilize a fixed point, leading to the onset of oscillatory behaviour. Next, we show for the choice of a Heaviside nonlinearity for the firing rate that such emergent oscillations can be either synchronous or anti-synchronous, depending on whether inhibition or excitation dominates the network architecture. To probe the behaviour of smooth (sigmoidal) nonlinear firing rates, we use a mixture of numerical bifurcation analysis and direct simulations, and uncover parameter windows that support chaotic behaviour. Finally, we comment on the role of delays in the generation of bursting oscillations, and discuss natural extensions of the work in this paper.

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Neural Activity in Primate Caudate Nucleus Associated With Pro- and Antisaccades

Journal of Neurophysiology ◽

10.1152/jn.00125.2009 ◽

2009 ◽

Vol 102 (4) ◽

pp. 2334-2341 ◽

Cited By ~ 32

Author(s):

Kristen A. Ford ◽

Stefan Everling

Keyword(s):

Caudate Nucleus ◽

Discharge Rate ◽

Indirect Pathway ◽

Behavioral Context ◽

Firing Rates ◽

Neuronal Populations ◽

Input Structure ◽

Flexible Behavior ◽

Two Populations

The basal ganglia (BG) play a central role in movement and it has been demonstrated that the discharge rate of neurons in these structures are modulated by the behavioral context of a given task. Here we used the antisaccade task, in which a saccade toward a flashed visual stimulus must be inhibited in favor of a saccade to the opposite location, to investigate the role of the caudate nucleus, a major input structure of the BG, in flexible behavior. In this study, we recorded extracellular neuronal activity while monkeys performed pro- and antisaccade trials. We identified two populations of neurons: those that preferred contralateral saccades (CSNs) and those that preferred ipsilateral saccades (ISNs). CSNs increased their firing rates for prosaccades, but not for antisaccades, and ISNs increased their firing rates for antisaccades, but not for prosaccades. We propose a model in which CSNs project to the direct BG pathway, facilitating saccades, and ISNs project to the indirect pathway, suppressing saccades. This model suggests one possible mechanism by which these neuronal populations could be modulating activity in the superior colliculus.

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Effect of time delay on the synchronization of excitatory-inhibitory neural networks

10.1101/2020.08.30.274662 ◽

2020 ◽

Author(s):

Hwayeon Ryu ◽

Sue Ann Campbell

Keyword(s):

Neural Networks ◽

Multiple Equilibria ◽

Necessary Conditions ◽

Inhibitory Neuron ◽

Synaptic Coupling ◽

Oscillatory State ◽

Numerical Bifurcation ◽

Type Of Behavior ◽

Numerical Bifurcation Analysis

AbstractWe 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 neuronal networks.

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Filaments and the Solar Dynamo

International Astronomical Union Colloquium ◽

10.1017/s0252921100048016 ◽

1998 ◽

Vol 167 ◽

pp. 406-414

Author(s):

N. Seehafer

Keyword(s):

Mean Field ◽

Decisive Role ◽

Dynamo Theory ◽

Simultaneous Generation ◽

Alpha Effect ◽

Generation Region ◽

The Mean ◽

Numerical Bifurcation ◽

Dynamo Effect

AbstractFilaments are a global phenomenon and their formation, structure and dynamics are determined by magnetic fields. So they are an important signature of the solar magnetism. The central mechanism in traditional mean-field dynamo theory is the alpha effect and it is a major result of this theory that the presence of kinetic or magnetic helicities is at least favourable for the effect. Recent studies of the magnetohydrodynamic equations by means of numerical bifurcation-analysis techniques have confirmed the decisive role of helicity for a dynamo effect. The alpha effect corresponds to the simultaneous generation of magnetic helicities in the mean field and in the fluctuations, the generation rates being equal in magnitude and opposite in sign. In the case of statistically stationary and homogeneous fluctuations, in particular, the alpha effect can increase the energy in the mean magnetic field only under the condition that also magnetic helicity is accumulated there. Generally, the two helicities generated by the alpha effect, that in the mean field and that in the fluctuations, have either to be dissipated in the generation region or to be transported out of this region. The latter may lead to the appearance of helicity in the atmosphere, in particular in filaments, and thus provide valuable information on dynamo processes inaccessible to in situ measurements.

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NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127401002407 ◽

2001 ◽

Vol 11 (03) ◽

pp. 737-753 ◽

Cited By ~ 19

Author(s):

TATYANA LUZYANINA ◽

KOEN ENGELBORGHS ◽

DIRK ROOSE

Keyword(s):

Differential Equations ◽

Bifurcation Analysis ◽

Delay Differential Equations ◽

Constant Delay ◽

State Dependent ◽

State Dependent Delay ◽

Numerical Bifurcation ◽

Delay Differential ◽

Steady State Solutions ◽

Numerical Bifurcation Analysis

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

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Numerical Bifurcation Analysis of Delayed Recycle Stream in a Continuously Stirred Tank Reactor

10.1063/1.3516300 ◽

2010 ◽

Author(s):

Nalwala Rohitbabu Gangadhar ◽

Periyasamy Balasubramanian ◽

Swapan Paruya ◽

Samarjit Kar ◽

Suchismita Roy

Keyword(s):

Bifurcation Analysis ◽

Stirred Tank ◽

Stirred Tank Reactor ◽

Tank Reactor ◽

Continuously Stirred Tank Reactor ◽

Numerical Bifurcation ◽

Numerical Bifurcation Analysis

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Changes in gamma-aminobutyric acid and somatostatin in epileptic cortex associated with low-grade gliomas

Journal of Neurosurgery ◽

10.3171/jns.1992.77.2.0209 ◽

1992 ◽

Vol 77 (2) ◽

pp. 209-216 ◽

Cited By ~ 106

Author(s):

Michael M. Haglund ◽

Mitchel S. Berger ◽

Dennis D. Kunkel ◽

JoAnn E. Franck ◽

Saadi Ghatan ◽

...

Keyword(s):

Epileptiform Activity ◽

Aminobutyric Acid ◽

Low Grade ◽

Tumor Infiltration ◽

Gamma Aminobutyric Acid ◽

Content Type ◽

Low Grade Gliomas ◽

Neuronal Populations ◽

Significant Difference

✓ The role of specific neuronal populations in epileptic foci was studied by comparing epileptic and nonepileptic cortex removed from patients with low-grade gliomas. Epileptic and nearby (within 1 to 2 cm) nonepileptic temporal lobe neocortex was identified using electrocorticography. Cortical specimens taken from four patients identified as epileptic and nonepileptic were all void of tumor infiltration. Somatostatin- and γ-aminobutyric acid (GABAergic)-immunoreactive neurons were identified and counted. Although there was no significant difference in the overall cell count, the authors found a significant decrease in both somatostatin- and GABAergic-immunoreactive neurons (74% and 51 %, respectively) in the epileptic cortex compared to that in nonepileptic cortex from the same patient. It is suggested that these findings demonstrate changes in neuronal subpopulations that may account for the onset and propagation of epileptiform activity in patients with low-grade gliomas.

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Spatial integration of mechanical forces by alpha-actinin establishes actin network symmetry

10.1101/578799 ◽

2019 ◽

Cited By ~ 1

Author(s):

Fabrice Senger ◽

Amandine Pitaval ◽

Hajer Ennomani ◽

Laetitia Kurzawa ◽

Laurent Blanchoin ◽

...

Keyword(s):

Network Architecture ◽

Spatial Organization ◽

Global Network ◽

Mechanical Forces ◽

Spatial Integration ◽

Actin Network ◽

Entire Cell ◽

Extracellular Microenvironment ◽

Extracellular Environment

Cell and tissue morphogenesis depend on the production and spatial organization of tensional forces in the actin cytoskeleton. Actin network architecture is complex because it is made of distinct modules in which filaments adopt a variety of organizations. The assembly and dynamics of these modules is well described but the self-organisation rules directing the global network architecture are much less understood. Here we investigated the mechanism regulating the interplay between network architecture and the geometry of cell’s extracellular environment. We found that α-actinin, a filament crosslinker, is essential for network symmetry to be consistent with extracellular microenvironment symmetry. It appeared to be required for the interconnection of transverse arcs with radial fibres to ensure an appropriate balance between forces at cell adhesions and across the entire actin network. Furthermore, the connectivity of the actin network appeared necessary for the cell ability to integrate and adapt to complex patterns of extracellular cues as they migrate. Altogether, our study has unveiled a role of actin-filament crosslinking in the physical integration of mechanical forces throughout the entire cell, and the role of this integration in the establishment and adaptation of intracellular symmetry axes in accordance with the geometry of extracellular cues.

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