MAP BASED MODELS IN NEURODYNAMICS

2010 ◽  
Vol 20 (06) ◽  
pp. 1631-1651 ◽  
Author(s):  
M. COURBAGE ◽  
V. I. NEKORKIN
Keyword(s):  
Dynamical Systems ◽  
Neural Activity ◽  
Single Neuron ◽  
Chaotic Attractors ◽  
Important Class ◽  
Mechanism Of Formation ◽  
Dynamical Mechanism ◽  
Subthreshold Oscillations ◽  
Basic Activity ◽  
Bursting Activity

This tutorial reviews a new important class of mathematical phenomenological models of neural activity generated by iterative dynamical systems: the so-called map-based systems. We focus on 1-D and 2-D maps for the replication of many features of the neural activity of a single neuron. It was shown that such systems can reproduce the basic activity modes such as spiking, bursting, chaotic spiking-bursting, subthreshold oscillations, tonic and phasic spiking, normal excitability, etc. of the real biological neurons. We emphasize on the representation of chaotic spiking-bursting oscillations by chaotic attractors of 2-D models. We also explain the dynamical mechanism of formation of such attractors and transition from one mode to another. We briefly present some synchronization mehanisms of chaotic spiking-bursting activity for two coupled neurons described by 1-D maps.

scholarly journals Spatio-temporal structure of single neuron subthalamic activity in Tourette Syndrome explored during DBS procedures

2019 ◽  
Author(s):  
Matteo Vissani ◽  
Roberto Cordella ◽  
Silvestro Micera ◽  
Luigi M. Romito ◽  
Alberto Mazzoni
Keyword(s):  
Firing Rate ◽  
Tourette Syndrome ◽  
Subthalamic Nucleus ◽  
Neural Activity ◽  
Single Neuron ◽  
Temporal Structure ◽  
Single Units ◽  
List Type ◽  
First Time ◽  
Bursting Activity

AbstractBasal ganglia dysfunctions have been suggested to play a causal role in the pathophysiology of most motor and non-motor symptoms of movement disorders as Tourette Syndrome (TS) or Parkinson’s Disease (PD). Intra/post-operative recordings from the subthalamic nucleus (STN) during Deep Brain Stimulation (DBS) procedures in PD patients have highlighted specific pathological patterns of neural activity. Spatial and temporal patterns of STN neural activity in TS are still unknown due to the lack of direct microrecordings in humans. Here, we describe for the first time specific neural activities of sensorimotor STN in TS patients, as recorded during intraoperative microrecordings. We analyzed 125 single units at 0.5 mm-spaced depths from the STN of anesthetized TS patients and we observed a large fraction of units (39/125, 31.2%) intensely bursting in the delta band (<4 Hz). In anesthetized PD patients we found similar average firing rate and spectral density of STN units, but differently to TS patients, only 4/54 (7.4%) of the units displayed bursting. Remarkably, bursting units in TS STN were not homogeneously distributed over the dorso-ventral trajectory of the recording: the highest density of bursting units was reliably found at the depth for which the clinical effect was maximal. Our results provide an unprecedented characterization of STN functional architecture and single units dynamics in TS patients, paving the way to an understanding of the role of STN subterritories in TS.Key PointsSingle neuron activity in Subthalamic Nucleus (STN) of patients with Tourette Syndrome (TS) was analyzed for the first time in literature.Firing rate and spectral content of single STN neurons in TS patients were found to be similar to those of anesthetized PD patients, while the analysis of arrhythmic bursting activity revealed that in TS patients the STN is characterized by a larger fraction of bursting neurons and more intense burstsBursting activity in TS was widespread across the whole STN, but with a higher density at the optimal lead location depth for DBS

Pulse Inputs Affect Timings of Spikes in Neurons with or Without Time Delays

2019 ◽  
Vol 20 (3-4) ◽  
pp. 257-267
Author(s):  
Jiaoyan Wang ◽  
Xiaoshan Zhao ◽  
Chao Lei
Keyword(s):  
Time Delays ◽  
Single Neuron ◽  
Spiking Neurons ◽  
Phase Resetting ◽  
Subthreshold Oscillations ◽  
Weak Pulse

AbstractInputs can change timings of spikes in neurons. But it is still not clear how input’s parameters for example injecting time of inputs affect timings of neurons. HR neurons receiving both weak and strong inputs are considered. How pulse inputs affecting neurons is studied by using the phase-resetting curve technique. For a single neuron, weak pulse inputs may advance or delay the next spike, while strong pulse inputs may induce subthreshold oscillations depending on parameters such as injecting timings of inputs. The behavior of synchronization in a network with or without coupling delays can be predicted by analysis in a single neuron. Our results can be used to predict the effects of inputs on other spiking neurons.

scholarly journals Omitted Variable Bias in GLMs of Neural Spiking Activity

2018 ◽  
Vol 30 (12) ◽  
pp. 3227-3258 ◽  
Author(s):  
Ian H. Stevenson
Keyword(s):  
Neural Activity ◽  
Single Neuron ◽  
Linear Models ◽  
Theory And Practice ◽  
Parameter Estimates ◽  
Omitted Variables ◽  
History Effects ◽  
Omitted Variable Bias ◽  
Wide Range ◽  
Variable Bias

Generalized linear models (GLMs) have a wide range of applications in systems neuroscience describing the encoding of stimulus and behavioral variables, as well as the dynamics of single neurons. However, in any given experiment, many variables that have an impact on neural activity are not observed or not modeled. Here we demonstrate, in both theory and practice, how these omitted variables can result in biased parameter estimates for the effects that are included. In three case studies, we estimate tuning functions for common experiments in motor cortex, hippocampus, and visual cortex. We find that including traditionally omitted variables changes estimates of the original parameters and that modulation originally attributed to one variable is reduced after new variables are included. In GLMs describing single-neuron dynamics, we then demonstrate how postspike history effects can also be biased by omitted variables. Here we find that omitted variable bias can lead to mistaken conclusions about the stability of single-neuron firing. Omitted variable bias can appear in any model with confounders—where omitted variables modulate neural activity and the effects of the omitted variables covary with the included effects. Understanding how and to what extent omitted variable bias affects parameter estimates is likely to be important for interpreting the parameters and predictions of many neural encoding models.

Generating Fully Bounded Chaotic Attractors

2013 ◽  
pp. 148-153
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Properties ◽  
The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

On different families of hidden chaotic attractors in fractional order dynamical systems

2018 ◽  
Author(s):  
Samuel Giovanni Hernandez-Orbe ◽  
Jess Manuel Muoz-Pacheco ◽  
German Ardl Munoz-Hernandez ◽  
Ernesto Zambrano-Serrano
Keyword(s):  
Dynamical Systems ◽  
Fractional Order ◽  
Chaotic Attractors

THE THEORY OF CONFINORS IN CHUA’S CIRCUIT: ACCURATE ANALYSIS OF BIFURCATIONS AND ATTRACTORS

1993 ◽  
Vol 03 (02) ◽  
pp. 333-361 ◽  
Author(s):  
RENÉ LOZI ◽  
SHIGEHIRO USHIKI
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Phase Portrait ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Bifurcation Diagrams ◽  
Accurate Analysis ◽  
Chua's Circuit

We apply the new concept of confinors and anti-confinors, initially defined for ordinary differential equations constrained on a cusp manifold, to the equations governing the circuit dynamics of Chua’s circuit. We especially emphasize some properties of the confinors of Chua’s equation with respect to the patterns in the time waveforms. Some of these properties lead to a very accurate numerical method for the computation of the half-Poincaré maps which reveal the precise structures of Chua’s strange attractors and the exact bifurcation diagrams with the help of a special sequence of change of coordinates. We also recall how such accurate methods allow the reliable numerical observation of the coexistence of three distinct chaotic attractors for at least one choice of the parameters. Chua’s equation seemssurprisingly rich in very new behaviors not yet reported even in other dynamical systems. The application of the theory of confinors to Chua’s equation and the use of sequences of Taylor’s coordinates could give new perspectives to the study of dynamical systems by uncovering very unusual behaviors not yet reported in the literature. The main paradox here is that the theory of confinors, which could appear as a theory of rough analysis of the phase portrait of Chua’s equation, leads instead to a very accurate analysis of this phase portrait.

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