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 Coherent and intermittent ensemble oscillations emerge from networks of irregular spiking neurons

2016 ◽  
Vol 115 (1) ◽  
pp. 457-469 ◽  
Author(s):  
Mahmood S. Hoseini ◽  
Ralf Wessel
Keyword(s):  
Single Neuron ◽  
Experimental Studies ◽  
Field Potential ◽  
Gamma Oscillations ◽  
Peak Frequency ◽  
Spiking Neurons ◽  
Network Activity ◽  
Cortical Circuits ◽  
Model Network ◽  
Low Rate

Local field potential (LFP) recordings from spatially distant cortical circuits reveal episodes of coherent gamma oscillations that are intermittent, and of variable peak frequency and duration. Concurrently, single neuron spiking remains largely irregular and of low rate. The underlying potential mechanisms of this emergent network activity have long been debated. Here we reproduce such intermittent ensemble oscillations in a model network, consisting of excitatory and inhibitory model neurons with the characteristics of regular-spiking (RS) pyramidal neurons, and fast-spiking (FS) and low-threshold spiking (LTS) interneurons. We find that fluctuations in the external inputs trigger reciprocally connected and irregularly spiking RS and FS neurons in episodes of ensemble oscillations, which are terminated by the recruitment of the LTS population with concurrent accumulation of inhibitory conductance in both RS and FS neurons. The model qualitatively reproduces experimentally observed phase drift, oscillation episode duration distributions, variation in the peak frequency, and the concurrent irregular single-neuron spiking at low rate. Furthermore, consistent with previous experimental studies using optogenetic manipulation, periodic activation of FS, but not RS, model neurons causes enhancement of gamma oscillations. In addition, increasing the coupling between two model networks from low to high reveals a transition from independent intermittent oscillations to coherent intermittent oscillations. In conclusion, the model network suggests biologically plausible mechanisms for the generation of episodes of coherent intermittent ensemble oscillations with irregular spiking neurons in cortical circuits.

Dynamics of globally delay-coupled neurons displaying subthreshold oscillations

2009 ◽  
Vol 367 (1901) ◽  
pp. 3255-3266 ◽  
Author(s):  
Cristina Masoller ◽  
M. C. Torrent ◽  
Jordi García-Ojalvo
Keyword(s):  
Coupled Oscillators ◽  
Single Neuron ◽  
Abrupt Change ◽  
Mean Field ◽  
Flip Bifurcation ◽  
Natural Period ◽  
Subthreshold Oscillations ◽  
The Common ◽  
Global Coupling ◽  
The Individual

We study an ensemble of neurons that are coupled through their time-delayed collective mean field. The individual neuron is modelled using a Hodgkin–Huxley-type conductance model with parameters chosen such that the uncoupled neuron displays autonomous subthreshold oscillations of the membrane potential. We find that the ensemble generates a rich variety of oscillatory activities that are mainly controlled by two time scales: the natural period of oscillation at the single neuron level and the delay time of the global coupling. When the neuronal oscillations are synchronized, they can be either in-phase or out-of-phase. The phase-shifted activity is interpreted as the result of a phase-flip bifurcation, also occurring in a set of globally delay-coupled limit cycle oscillators. At the bifurcation point, there is a transition from in-phase to out-of-phase (or vice versa) synchronized oscillations, which is accompanied by an abrupt change in the common oscillation frequency. This phase-flip bifurcation was recently investigated in two mutually delay-coupled oscillators and can play a role in the mechanisms by which the neurons switch among different firing patterns.

Multidimensional Encoding Strategy of Spiking Neurons

2000 ◽  
Vol 12 (7) ◽  
pp. 1519-1529 ◽  
Author(s):  
Christian W. Eurich ◽  
Stefan D. Wilke
Keyword(s):  
Single Neuron ◽  
Population Based ◽  
Spiking Neurons ◽  
Neural Population ◽  
Neural Responses ◽  
Tuning Curves ◽  
Tuning Width ◽  
Optimal Encoding ◽  
Stimulus Features ◽  
Encoding Strategy

Neural responses in sensory systems are typically triggered by a multitude of stimulus features. Using information theory, we study the encoding accuracy of a population of stochastically spiking neurons characterized by different tuning widths for the different features. The optimal encoding strategy for representing one feature most accurately consists of narrow tuning in the dimension to be encoded, to increase the single-neuron Fisher information, and broad tuning in all other dimensions, to increase the number of active neurons. Extremely narrow tuning without sufficient receptive field overlap will severely worsen the coding. This implies the existence of an optimal tuning width for the feature to be encoded. Empirically, only a subset of all stimulus features will normally be accessible. In this case, relative encoding errors can be calculated that yield a criterion for the function of a neural population based on the measured tuning curves.

Stability and Hopf Bifurcation Analysis in Hindmarsh–Rose Neuron Model with Multiple Time Delays

2016 ◽  
Vol 26 (11) ◽  
pp. 1650187 ◽  
Author(s):  
Dongpo Hu ◽  
Hongjun Cao
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Time Delays ◽  
Single Neuron ◽  
Neuron Model ◽  
Multiple Time ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
Multiple Time Delays ◽  
The Stability

In this paper, the dynamical behaviors of a single Hindmarsh–Rose neuron model with multiple time delays are investigated. By linearizing the system at equilibria and analyzing the associated characteristic equation, the conditions for local stability and the existence of local Hopf bifurcation are obtained. To discuss the properties of Hopf bifurcation, we derive explicit formulas to determine the direction of Hopf bifurcation and the stability of bifurcated periodic solutions occurring through Hopf bifurcation. The qualitative analyses have demonstrated that the values of multiple time delays can affect the stability of equilibrium and play an important role in determining the properties of Hopf bifurcation. Some numerical simulations are given for confirming the qualitative results. Numerical simulations on the effect of delays show that the delays have different scales when the two delay values are not equal. The physiological basis is most likely that Hindmarsh–Rose neuron model has two different time scales. Finally, the bifurcation diagrams of inter-spike intervals of the single Hindmarsh–Rose neuron model are presented. These bifurcation diagrams show the existence of complex bifurcation structures and further indicate that the multiple time delays are very important parameters in determining the dynamical behaviors of the single neuron. Therefore, these results in this paper could be helpful for further understanding the role of multiple time delays in the information transmission and processing of a single neuron.

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.

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