Dynamic Analysis and Simulation for Two Different Chaos-Like Stochastic Neural Firing Patterns Observed in Real Biological System

2017 ◽  
pp. 749-757 ◽  
Author(s):  
Huijie Shang ◽  
Rongbin Xu ◽  
Dong Wang
Keyword(s):  
Dynamic Analysis ◽  
Biological System ◽  
Neural Firing ◽  
Firing Patterns

IDENTIFYING DISTINCT STOCHASTIC DYNAMICS FROM CHAOS: A STUDY ON MULTIMODAL NEURAL FIRING PATTERNS

2009 ◽  
Vol 19 (02) ◽  
pp. 453-485 ◽  
Author(s):  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
LI LI ◽  
YULIN XU ◽  
HONGJV LIU ◽  
...  
Keyword(s):  
Time Series ◽  
Limit Cycle ◽  
Stochastic Dynamics ◽  
Nonlinear Time Series ◽  
Special Importance ◽  
Neuronal System ◽  
Neural Firing ◽  
Firing Patterns ◽  
Theoretical Simulation ◽  
Definition Of

Some chaotic and a series of stochastic neural firings are multimodal. Stochastic multimodal firing patterns are of special importance because they indicate a possible utility of noise. A number of previous studies confused the dynamics of chaotic and stochastic multimodal firing patterns. The confusion resulted partly from inappropriate interpretations of estimations of nonlinear time series measures. With deliberately chosen examples the present paper introduces strategies and methods of identification of stochastic firing patterns from chaotic ones. Aided by theoretical simulation we show that the stochastic multimodal firing patterns result from the effects of noise on neuronal systems near to a bifurcation between two simpler attractors, such as a point attractor and a limit cycle attractor or two limit cycle attractors. In contrast, the multimodal chaotic firing trains are generated by the dynamics of a specific strange attractor. Three systems were carefully chosen to elucidate these two mechanisms. An experimental neural pacemaker model and the Chay mathematical model were used to show the stochastic dynamics, while the deterministic Wang model was used to show the deterministic dynamics. The usage and interpretation of nonlinear time series measures were systematically tested by applying them to firing trains generated by the three systems. We successfully identified the distinct differences between stochastic and chaotic multimodal firing patterns and showed the dynamics underlying two categories of stochastic firing patterns. The first category results from the effects of noise on the neuronal system near a Hopf bifurcation. The second category results from the effects of noise on the period-adding bifurcation between two limit cycles. Although direct application of nonlinear measures to interspike interval series of these firing trains misleadingly implies chaotic properties, definition of eigen events based on more appropriate judgments of the underlying dynamics leads to accurate identifications of the stochastic properties.

Analysis of Firing Patterns in Single Neurons

Science ◽  
1960 ◽  
Vol 131 (3416) ◽  
pp. 1811-1812 ◽  
Author(s):  
George L. Gerstein
Keyword(s):  
Spontaneous Activity ◽  
Digital Computer ◽  
High Speed ◽  
High Sensitivity ◽  
Single Neurons ◽  
Neural Firing ◽  
Firing Patterns ◽  
Stimulus Response

The use of a high-speed digital computer for investigation of neural firing patterns is described. The high sensitivity of the method permits detection of stimulus-response relations buried in a background of spontaneous activity.

COHERENCE RESONANCE–INDUCED STOCHASTIC NEURAL FIRING AT A SADDLE-NODE BIFURCATION

2011 ◽  
Vol 25 (29) ◽  
pp. 3977-3986 ◽  
Author(s):  
HUAGUANG GU ◽  
HUIMIN ZHANG ◽  
CHUNLING WEI ◽  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Firing Pattern ◽  
Neuronal System ◽  
Neural Firing ◽  
Coherence Resonance ◽  
Saddle Node Bifurcation ◽  
Hopf Bifurcation Point ◽  
Firing Patterns ◽  
Saddle Node

Coherence resonance at a saddle-node bifurcation point and the corresponding stochastic firing patterns are simulated in a theoretical neuronal model. The characteristics of noise-induced neural firing pattern, such as exponential decay in histogram of interspike interval (ISI) series, independence and stochasticity within ISI series are identified. Firing pattern similar to the simulated results was discovered in biological experiment on a neural pacemaker. The difference between this firing and integer multiple firing generated at a Hopf bifurcation point is also given. The results not only revealed the stochastic dynamics near a saddle-node bifurcation, but also gave practical approaches to identify the saddle-node bifurcation and to distinguish it from the Hopf bifurcation in neuronal system. In addition, many previously observed firing patterns can be attribute to stochastic firing pattern near such a saddle-node bifurcation.

DIFFERENT BIFURCATION SCENARIOS OF NEURAL FIRING PATTERNS OBSERVED IN THE BIOLOGICAL EXPERIMENT ON IDENTICAL PACEMAKERS

2013 ◽  
Vol 23 (12) ◽  
pp. 1350195 ◽  
Author(s):  
HUAGUANG GU
Keyword(s):  
Parameter Space ◽  
Period Doubling ◽  
Two Dimensional ◽  
Neural Firing ◽  
Biological Experiment ◽  
Dimensional Parameter ◽  
Simple Process ◽  
Firing Patterns ◽  
Complex Process ◽  
Different Levels

Two different bifurcation scenarios of spontaneous neural firing patterns with decreasing extracellular calcium concentrations were observed in the biological experiment on identical pacemakers when potassium concentrations were fixed at two different levels. Six typical experimental scenarios manifesting dynamics closely matching those previously simulated using the Hindmarsh–Rose model and Chay model are provided as representative examples. Bifurcation scenarios from period-1 bursting to period-1 spiking via a complex process and via a simple process, period-doubling bifurcation to chaos, period-adding bifurcation with chaos, and period-adding bifurcation with stochastic burstings were identified. The results not only reveal that an experimental neural pacemaker is capable of generating different bifurcation scenarios but also provide a basic framework for bifurcations in neural firing patterns in a two-dimensional parameter space.

Understanding of physiological neural firing patterns through dynamical bifurcation machineries

Neuroreport ◽  
2006 ◽  
Vol 17 (10) ◽  
pp. 995-999 ◽  
Author(s):  
Minghao Yang ◽  
Shucheng An ◽  
Huaguang Gu ◽  
Zhiqiang Liu ◽  
Wei Ren
Keyword(s):  
Neural Firing ◽  
Firing Patterns

Information-Geometric Measure for Neural Spikes

2002 ◽  
Vol 14 (10) ◽  
pp. 2269-2316 ◽  
Author(s):  
Hiroyuki Nakahara ◽  
Shun-ichi Amari
Keyword(s):  
Information Geometry ◽  
Higher Order ◽  
Neural Firing ◽  
Firing Patterns ◽  
Neural Spikes ◽  
Geometric Measure ◽  
Leibler Divergence ◽  
Novel Method ◽  
Account Information ◽  
Spike Firing

This study introduces information-geometric measures to analyze neural firing patterns by taking not only the second-order but also higher-order interactions among neurons into account. Information geometry provides useful tools and concepts for this purpose, including the orthogonality of coordinate parameters and the Pythagoras relation in the Kullback-Leibler divergence. Based on this orthogonality, we show a novel method for analyzing spike firing patterns by decomposing the interactions of neurons of various orders. As a result, purely pairwise, triple-wise, and higher-order interactions are singled out. We also demonstrate the benefits of our proposal by using several examples.

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