Averaging, Folded Singularities, and Torus Canards: Explaining Transitions between Bursting and Spiking in a Coupled Neuron Model

2015 ◽  
Vol 14 (4) ◽  
pp. 1808-1844 ◽  
Author(s):  
Kerry-Lyn Roberts ◽  
Jonathan E. Rubin ◽  
Martin Wechselberger
Keyword(s):  
Neuron Model ◽  
Torus Canards

scholarly journals Механизмы перехода от ритмической активности к пачечной в модели ноцицептивного нейрона

2020 ◽  
Vol 90 (3) ◽  
pp. 501
Author(s):  
О.Е. Дик
Keyword(s):  
Bifurcation Diagram ◽  
Neuron Model ◽  
Nociceptive Neuron ◽  
Fast Subsystem ◽  
Full System ◽  
Stimulus Value ◽  
Special Solutions ◽  
Limit Cycle Bifurcation ◽  
Torus Canards ◽  
Torus Bifurcation

The transitions from tonic spiking to bursting for the nociceptive neuron model have been studied with changing the external stimulus value. The presence of the fold limit cycle bifurcation in the structure of the bifurcation diagram of the fast subsystem and the torus bifurcation in the structure of the bifurcation diagram of the full system lead to the emergence of special solutions of the type torus canards in these transitions. This confirms the assumption that torus canards are an obligatory feature for transitions between rhythmic and burst discharges

Low Capacity Implementation of a Pulse-Type Chaotic Neuron Model

2016 ◽  
Vol 136 (10) ◽  
pp. 1424-1430 ◽  
Author(s):  
Yoshiki Sasaki ◽  
Katsutoshi Saeki ◽  
Yoshifumi Sekine
Keyword(s):  
Neuron Model ◽  
Pulse Type ◽  
Chaotic Neuron

scholarly journals Canonical models for torus canards in elliptic bursters

2021 ◽  
Vol 31 (6) ◽  
pp. 063129
Author(s):  
E. Baspinar ◽  
D. Avitabile ◽  
M. Desroches
Keyword(s):  
Canonical Models ◽  
Torus Canards

scholarly journals Exploiting heterogeneity in operational neural networks by synaptic plasticity

2021 ◽  
Author(s):  
Serkan Kiranyaz ◽  
Junaid Malik ◽  
Habib Ben Abdallah ◽  
Turker Ince ◽  
Alexandros Iosifidis ◽  
...  
Keyword(s):  
Neural Networks ◽  
Synaptic Plasticity ◽  
Network Model ◽  
Neuron Model ◽  
Linear Operators ◽  
Training Data ◽  
Learning Performance ◽  
Minimal Network ◽  
Hidden Layer ◽  
Hidden Neurons

AbstractThe recently proposed network model, Operational Neural Networks (ONNs), can generalize the conventional Convolutional Neural Networks (CNNs) that are homogenous only with a linear neuron model. As a heterogenous network model, ONNs are based on a generalized neuron model that can encapsulate any set of non-linear operators to boost diversity and to learn highly complex and multi-modal functions or spaces with minimal network complexity and training data. However, the default search method to find optimal operators in ONNs, the so-called Greedy Iterative Search (GIS) method, usually takes several training sessions to find a single operator set per layer. This is not only computationally demanding, also the network heterogeneity is limited since the same set of operators will then be used for all neurons in each layer. To address this deficiency and exploit a superior level of heterogeneity, in this study the focus is drawn on searching the best-possible operator set(s) for the hidden neurons of the network based on the “Synaptic Plasticity” paradigm that poses the essential learning theory in biological neurons. During training, each operator set in the library can be evaluated by their synaptic plasticity level, ranked from the worst to the best, and an “elite” ONN can then be configured using the top-ranked operator sets found at each hidden layer. Experimental results over highly challenging problems demonstrate that the elite ONNs even with few neurons and layers can achieve a superior learning performance than GIS-based ONNs and as a result, the performance gap over the CNNs further widens.

scholarly journals Digital Implementation of the Two-Compartmental Pinsky–Rinzel Pyramidal Neuron Model

2018 ◽  
Vol 12 (1) ◽  
pp. 47-57 ◽  
Author(s):  
Elahe Rahimian ◽  
Soheil Zabihi ◽  
Mahmood Amiri ◽  
Bernabe Linares-Barranco
Keyword(s):  
Pyramidal Neuron ◽  
Neuron Model ◽  
Digital Implementation

COMPLEX BIFURCATION STRUCTURES IN THE HINDMARSH–ROSE NEURON MODEL

2007 ◽  
Vol 17 (09) ◽  
pp. 3071-3083 ◽  
Author(s):  
J. M. GONZÀLEZ-MIRANDA
Keyword(s):  
Phase Diagram ◽  
Bifurcation Diagram ◽  
Parameter Space ◽  
Neuron Model ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Rapid Responses ◽  
Bifurcation Structures

The results of a study of the bifurcation diagram of the Hindmarsh–Rose neuron model in a two-dimensional parameter space are reported. This diagram shows the existence and extent of complex bifurcation structures that might be useful to understand the mechanisms used by the neurons to encode information and give rapid responses to stimulus. Moreover, the information contained in this phase diagram provides a background to develop our understanding of the dynamics of interacting neurons.

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