scholarly journals Hamiltonian energy and coexistence of hidden firing patterns from bidirectional coupling between two different neurons

2021 ◽  
Author(s):  
Zeric Tabekoueng Njitacke ◽  
Bernard Nzoko Koumetio ◽  
Balamurali Ramakrishnan ◽  
Gervais Dolvis Leutcho ◽  
Theophile Fonzin Fozin ◽  
...  
Keyword(s):  
Analog Circuit ◽  
Synaptic Weight ◽  
Numerical Results ◽  
Electrical Synapse ◽  
Synaptic Coupling ◽  
Firing Patterns ◽  
Digital Implementation ◽  
Pspice Simulations ◽  
Chaotic Bursting ◽  
Electrical Activities

AbstractIn this paper, bidirectional-coupled neurons through an asymmetric electrical synapse are investigated. These coupled neurons involve 2D Hindmarsh–Rose (HR) and 2D FitzHugh–Nagumo (FN) neurons. The equilibria of the coupled neurons model are investigated, and their stabilities have revealed that, for some values of the electrical synaptic weight, the model under consideration can display either self-excited or hidden firing patterns. In addition, the hidden coexistence of chaotic bursting with periodic spiking, chaotic spiking with period spiking, chaotic bursting with a resting pattern, and the coexistence of chaotic spiking with a resting pattern are also found for some sets of electrical synaptic coupling. For all the investigated phenomena, the Hamiltonian energy of the model is computed. It enables the estimation of the amount of energy released during the transition between the various electrical activities. Pspice simulations are carried out based on the analog circuit of the coupled neurons to support our numerical results. Finally, an STM32F407ZE microcontroller development board is exploited for the digital implementation of the proposed coupled neurons model.

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

2008 ◽  
Vol 24 (6) ◽  
pp. 593-628 ◽  
Author(s):  
Qishao Lu ◽  
Huaguang Gu ◽  
Zhuoqin Yang ◽  
Xia Shi ◽  
Lixia Duan ◽  
...  
Keyword(s):  
Firing Patterns ◽  
Electrical Activities

scholarly journals Smooth Nonlinear Fitting Scheme for Analog Multiplierless Implementation of Hindmarsh-Rose Neuron Model

2021 ◽  
Author(s):  
Jianming Cai ◽  
Han Bao ◽  
Quan Xu ◽  
Zhongyun Hua ◽  
Bocheng Bao
Keyword(s):  
Large Scale ◽  
Neuron Model ◽  
Hardware Implementation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Implementation Cost ◽  
Hyperbolic Tangent ◽  
Nonlinear Fitting ◽  
Chaotic Bursting ◽  
Electrical Activities

Abstract The Hindmarsh-Rose (HR) neuron model is built to describe the neuron electrical activities. Due to the polynomial nonlinearities, multipliers are required to implement the HR neuron model in analog. In order to avoid the multipliers, this brief presents a novel smooth nonlinear fitting scheme. We first construct two nonlinear fitting functions using the composite hyperbolic tangent functions and then implement an analog multiplierless circuit for the two-dimensional (2D) or three- dimensional (3D) HR neuron model. To exhibit the nonlinear fitting effects, numerical simulations and hardware experiments for the fitted HR neuron model are provided successively. The results show that the fitted HR neuron model with analog multiplierless circuit can display different operation patterns of resting, periodic spiking, and periodic/chaotic bursting, entirely behaving like the original HR neuron model. The analog multiplierless circuit has the advantage of low implementation cost and thereby it might be suitable for the hardware implementation of large-scale neural networks.

Abundant Firing Patterns in a Memristive Morris–Lecar Neuron Model

2021 ◽  
Vol 31 (11) ◽  
pp. 2150170
Author(s):  
Guoyuan Qi ◽  
Yu Wu ◽  
Jianbing Hu
Keyword(s):  
Cell Membrane ◽  
Electromagnetic Fields ◽  
Neuron Model ◽  
Brain Activity ◽  
Neuronal Cell ◽  
Distinct Pattern ◽  
Magnetic Field Effects ◽  
Firing Patterns ◽  
Electrical Activities ◽  
Electronic Implementation

Improving the neuron model and studying its electrical activities according to the real biophysical environment are significant in human cognitive brain activity and neural behavior. The complex transmembrane motion of ions on the neuronal cell membrane can establish time-varying electromagnetic fields and affect the transition firing patterns of neurons. In this paper, a threshold memristor is used to describe the electromagnetic induction and magnetic field effects of neuron cell membrane ion exchange to improve the neuron model, and a memristive Morris–Lecar (mM–L) neuron model is proposed. Numerical simulation confirms that different intensities of electromagnetic fields can produce distinct pattern transitions in electrical activities of the neuron, such as periodic bursting, periodic spiking, chaotic bursting. From the perspective of neuron’s interspike interval (ISI), the ISIs bifurcation in the multiparameter planes, ISIs firing periods, the variance of ISIs and other methods are used to find the trend of the mM–L neuron firing pattern transition. Finally, based on the 4D nonlinear differential equation of the mM–L neuron model, the complete electronic implementation of the model is designed. The output of the designed circuit is consistent with the theoretical prediction, which is extremely useful for studying the dynamics of a single neuron.

THE BIFURCATION STRUCTURE OF FIRING PATTERN TRANSITIONS IN THE CHAY NEURONAL PACEMAKER MODEL

2008 ◽  
Vol 16 (01) ◽  
pp. 33-49 ◽  
Author(s):  
ZHUOQIN YANG ◽  
QISHAO LU
Keyword(s):  
Bifurcation Analysis ◽  
Calcium Concentration ◽  
Period Doubling ◽  
Nerve Fibers ◽  
Neuronal Firing ◽  
Dynamical Parameter ◽  
True Nature ◽  
Firing Patterns ◽  
Chaotic Bursting ◽  
Period Doubling Bifurcations

Different transitions of neuronal firing patterns are explored by the combination of experimental results, numerical simulation and bifurcation analysis. Three types of firing sequences with respect to extracellular calcium concentration ([ Ca 2+] o ) were observed in experiments on neural pacemakers. In accordance with them, the corresponding transitions of neuronal firing patterns are surveyed by standard bifurcation analysis of the Chay model, where λn corresponds to different nerve fibers and VC is the dynamical parameter. The results are listed in this paper. Firstly, it is obtained that the transitions of periodic firing patterns from period-1 bursting to period-1 spiking without any bifurcation, from period-1 to -2 to -1 through a pair of period-doubling bifurcations and from period-1 to -2 to -1 through two pairs of period-doubling bifurcations. Secondly, one supercritical and two subcritical period-doubling bursting sequences with different appearances lead to chaos, respectively. Then the former transits directly to an inverse supercritical period-doubling spiking sequence via chaos, and the latter transit to it through the period-adding bursting sequences from period-1 to -3 and from -1 to -5 with chaotic bursting, respectively. Thirdly, we reveal the true nature of period-adding bursting sequence without chaotic bursting. Every periodic bursting is closely related to two period-doubling bifurcations of the corresponding periodic spiking, except for period-1 bursting appearing via Hopf bifurcation and disappearing via period-doubling bifurcation. As a consequence, the period-adding bursting sequence without chaotic bursting has a compound structure of elementary bifurcations with transitions from spiking to bursting. Thus period-adding bifurcation without chaos cannot be regarded as a new elementary bifurcation.

Chaotic Bursting Dynamics and Coexisting Multistable Firing Patterns in 3D Autonomous Morris–Lecar Model and Microcontroller-Based Validations

2019 ◽  
Vol 29 (10) ◽  
pp. 1950134 ◽  
Author(s):  
Bocheng Bao ◽  
Qinfeng Yang ◽  
Lei Zhu ◽  
Han Bao ◽  
Quan Xu ◽  
...  
Keyword(s):  
Neuron Model ◽  
Phase Plane ◽  
Three Dimensional ◽  
Model Parameters ◽  
Fast Subsystem ◽  
Firing Patterns ◽  
Chaotic Bursting ◽  
Attraction Basins ◽  
Initial States ◽  
Electronic Neuron

A three-dimensional (3D) autonomous Morris–Lecar (simplified as M–L) neuron model with fast and slow structures was proposed to generate periodic bursting behaviors. However, chaotic bursting dynamics and coexisting multistable firing patterns have been rarely discussed in such a 3D M–L neuron model. For some specified model parameters, MATLAB numerical plots are executed by bifurcation plots, time sequences, phase plane plots, and 0–1 tests, from which diverse forms of chaotic bursting, chaotic tonic-spiking, and periodic bursting behaviors are uncovered in the 3D M–L neuron model. Furthermore, based on the theoretically constructing fold/Hopf bifurcation sets of the fast subsystem, the bifurcation mechanism for the chaotic bursting behaviors is thereby expounded qualitatively. Particularly, through numerically plotting the attraction basins related to the initial states under two sets of specific parameters, coexisting multistable firing patterns are demonstrated in the 3D M–L neuron model also. Finally, a digitally circuit-implemented electronic neuron is generated based on a low-power microcontroller and its experimentally captured results faultlessly validate the numerical plots.

Coexistence of firing patterns and its control in two neurons coupled through an asymmetric electrical synapse

2020 ◽  
Vol 30 (2) ◽  
pp. 023101 ◽  
Author(s):  
Z. Tabekoueng Njitacke ◽  
Isaac Sami Doubla ◽  
J. Kengne ◽  
A. Cheukem
Keyword(s):  
Electrical Synapse ◽  
Firing Patterns

Memristor Initial-Offset Boosting in Memristive HR Neuron Model with Hidden Firing Patterns

2020 ◽  
Vol 30 (10) ◽  
pp. 2030029
Author(s):  
Han Bao ◽  
Wenbo Liu ◽  
Jun Ma ◽  
Huagan Wu
Keyword(s):  
Neuron Model ◽  
Analog Circuit ◽  
Three Dimensional ◽  
Basins Of Attraction ◽  
Initial Value ◽  
Firing Patterns ◽  
Offset Boosting ◽  
Extreme Multistability ◽  
Flux Variable ◽  
Memristor Synapse

A new three-dimensional (3D) memristive HR neuron model is presented, which is improved from an existing memristive HR neuron model using a memristor synapse with sine memductance to substitute the original one. The improved memristive HR neuron model has no equilibrium but hidden firing activities can emerge with discrete memristor initial-offset boosting. Treating the neuron model as a two-dimensional (2D) major subsystem controlled by a magnetic flux variable, fold bifurcations for hidden chaotic and periodic firing patterns are elaborated. The coexistence of hidden firing patterns induced by memristor initial boosting is quantitatively analyzed and numerically simulated by bifurcation plots, phase plots, and basins of attraction. The results demonstrate that the improved memristive HR neuron model can exhibit a discrete memristor initial-offset boosting behavior owning infinitely many disconnected basins of attraction and the generating firing patterns can be boosted to different discrete levels by changing the memristor initial value, differing entirely from various boosting behaviors reported previously. Therefore, infinitely many hidden coexisting offset-boosted firing patterns with the same initial-offsets and attractor types are disclosed along the boosting route, which are homogenous with extreme multistability and are perfectly validated by PSIM circuit simulations based on a physically implementation-oriented analog circuit.

scholarly journals A Novel Chaotic System with Two Circles of Equilibrium Points: Multistability, Electronic Circuit and FPGA Realization

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1211 ◽  
Author(s):  
Sambas ◽  
Vaidyanathan ◽  
Tlelo-Cuautle ◽  
Zhang ◽  
Sukono ◽  
...  
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Digital Implementation ◽  
Gate Arrays ◽  
New Chaotic System ◽  
Field Programmable ◽  
Programmable Gate Arrays ◽  
Good Agreement

This paper introduces a new chaotic system with two circles of equilibrium points. The dynamical properties of the proposed dynamical system are investigated through evaluating Lyapunov exponents, bifurcation diagram and multistability. The qualitative study shows that the new system exhibits coexisting periodic and chaotic attractors for different values of parameters. The new chaotic system is implemented in both analog and digital electronics. In the former case, we introduce the analog circuit of the proposed chaotic system with two circles of equilibrium points using amplifiers, which is simulated in MultiSIM software, version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB. In addition, we perform the digital implementation of the new chaotic system using field-programmable gate arrays (FPGA), the experimental observations of the attractors of which confirm its suitability to generate chaotic behavior.

scholarly journals Bifurcation Scenarios of Neural Firing Patterns across Two Separated Chaotic Regions as Indicated by Theoretical and Biological Experimental Models

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Huaguang Gu ◽  
Baobao Pan ◽  
Jian Xu
Keyword(s):  
Period Doubling ◽  
Prediction Method ◽  
Experimental Models ◽  
Nonlinear Prediction ◽  
Neural Firing ◽  
Firing Patterns ◽  
Chaotic Bursting ◽  
Chaotic Region ◽  
Period 2 ◽  
Experimental Findings

Nonlinear dynamics can be used to identify relationships between different firing patterns, which play important roles in the information processing. The present study provides novel biological experimental findings regarding complex bifurcation scenarios from period-1 bursting to period-1 spiking with chaotic firing patterns. These bifurcations were found to be similar to those simulated using the Hindmarsh-Rose model across two separated chaotic regions. One chaotic region lay between period-1 and period-2 burstings. This region has not attracted much attention. The other region is a well-known comb-shaped chaotic region, and it appears after period-2 bursting. After period-2 bursting, the chaotic firings lay in a period-adding bifurcation scenario or in a period-doubling bifurcation cascade. The deterministic dynamics of the chaotic firing patterns were identified using a nonlinear prediction method. These results provided details regarding the processes and dynamics of bifurcation containing the chaotic bursting between period-1 and period-2 burstings and other chaotic firing patterns within the comb-shaped chaotic region. They also provided details regarding the relationships between different firing patterns in parameter space.

Difference Between Intermittent Chaotic Bursting and Spiking of Neural Firing Patterns

2014 ◽  
Vol 24 (06) ◽  
pp. 1450082 ◽  
Author(s):  
Huaguang Gu ◽  
Weiwei Xiao
Keyword(s):  
Deep Understanding ◽  
Slow Variable ◽  
Type I ◽  
Neural Firing ◽  
Firing Patterns ◽  
Return Map ◽  
Smooth Structures ◽  
Chaotic Bursting ◽  
Type V ◽  
Intermittent Chaos

The chaotic spiking and intermittent chaotic bursting were observed from biological experiment on a neural pacemaker. The intermittent chaotic bursting manifested alternation between a phase of nearly period-3 bursting and another phase of irregular bursting, and exhibited a nonsmooth-like structure in the first return map of interspike interval (ISI) series. The chaotic spiking manifested a smooth structure. The intermittent chaotic bursting and spiking simulated in the Chay model were identified by the dissection of the fast-slow variables. The intermittent chaotic bursting manifested nonsmooth-like structures in the first return map of both ISI and slow variable, while spiking exhibited smooth structures. The intermittent chaotic bursting and spiking manifested different scale laws of the averaged length of periodic phase with respect to the changes of parameter value. The scale law of bursting was similar to those of both type V intermittent chaos generated in a nonsmooth map and type I in a smooth system, while that of spiking resembled type I more than type V. The results revealed the dynamics of intermittent chaotic firing patterns, the differences between the intermittent chaotic bursting and spiking patterns and the relationships to the smooth and nonsmooth-like characteristics, provided a deep understanding of intermittent chaotic firing patterns, and indicated different mechanisms of the adjustment of variables from slow to fast between bursting and spiking patterns.

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