Dynamical Response of Electrical Activities in Digital Neuron Circuit Driven by Autapse

2017 ◽  
Vol 27 (12) ◽  
pp. 1750187 ◽  
Author(s):  
Guodong Ren ◽  
Ping Zhou ◽  
Jun Ma ◽  
Ning Cai ◽  
Ahmed Alsaedi ◽  
...  
Keyword(s):  
Electromagnetic Induction ◽  
Numerical Scheme ◽  
Neuron Model ◽  
Biological Function ◽  
Digital Circuit ◽  
Dynamical Analysis ◽  
Dynamical Response ◽  
Neuron Models ◽  
Model Driven ◽  
Electrical Activities

Neuron models are available for computational neurodynamics and the main dynamical properties can be reproduced in the numerical scheme for further dynamical analysis. During model setting, some important biophysical factors should be considered and thus reliable neuron models can be approached. In this paper, a neuron model driven by autapse connection is investigated with the effect of electromagnetic induction being considered as well. A digital neuronal circuit is designed by using FPGA, the dynamical response and biological function of autapse connection. It is found that positive feedback in autapse can modulate the oscillating behaviors in the digital circuit, which could be effective for further investigation on digital neuronal network.

The Electrical Activity of Neurons Subject to Electromagnetic Induction and Gaussian White Noise

2017 ◽  
Vol 27 (02) ◽  
pp. 1750030 ◽  
Author(s):  
Ya Wang ◽  
Jun Ma ◽  
Ying Xu ◽  
Fuqiang Wu ◽  
Ping Zhou
Keyword(s):  
Electromagnetic Induction ◽  
Gaussian White Noise ◽  
Theoretical Models ◽  
Ion Concentration ◽  
Dynamical Response ◽  
Induced Current ◽  
Neuron Models ◽  
Electrical Stimuli ◽  
Electrical Activities ◽  
Channel Currents

Neurons can give appropriate response to external electrical stimuli and the modes in electrical activities can be carefully selected. Most of the neuron models mainly emphasize on the ion channel currents embedded into the membrane and the properties in electrical activities can be produced in the theoretical models. Indeed, some physical effect should be considered during the model setting for neuronal activities. In fact, induced current and the electrical field will cause the membrane potential to change and an exchange of charged ions during the fluctuation of ion concentration in cell. As a result, the effect of electromagnetic induction should be seriously considered. In this paper, magnetic flux is proposed to describe the effect of electromagnetic field, and the memristor is used to realize coupling on membrane by inputting induced current based on consensus of physical unit. Noise is also considered to detect the dynamical response in electrical activities and stochastic resonance, it is found that multiple modes can be selected in the electrical activities and it could be associated with memory effect and self-adaption in neurons.

Dynamical analysis of Josephson junction neuron model driven by a thermal signal and its digital implementation based on microcontroller

2021 ◽  
Vol 94 (12) ◽  
Author(s):  
Noel Freddy Fotie Foka ◽  
Balamurali Ramakrishnan ◽  
André Rodrigue Tchamda ◽  
Sifeu Takougang Kingni ◽  
Karthikeyan Rajagopal ◽  
...  
Keyword(s):  
Josephson Junction ◽  
Neuron Model ◽  
Dynamical Analysis ◽  
Digital Implementation ◽  
Model Driven ◽  
Thermal Signal

Dynamical response, information transition and energy dependence in a neuron model driven by autapse

2017 ◽  
Vol 90 (4) ◽  
pp. 2893-2902 ◽  
Author(s):  
Yuan Yue ◽  
Liwei Liu ◽  
Yujiang Liu ◽  
Yong Chen ◽  
Yueling Chen ◽  
...  
Keyword(s):  
Energy Dependence ◽  
Neuron Model ◽  
Dynamical Response ◽  
Model Driven ◽  
Response Information

scholarly journals Three-Dimensional Memristive Hindmarsh–Rose Neuron Model with Hidden Coexisting Asymmetric Behaviors

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Bocheng Bao ◽  
Aihuang Hu ◽  
Han Bao ◽  
Quan Xu ◽  
Mo Chen ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Electromagnetic Induction ◽  
Neuron Model ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Neuronal System ◽  
System A ◽  
Dynamical Behaviors ◽  
Electrical Activities

Since the electrical activities of neurons are closely related to complex electrophysiological environment in neuronal system, a novel three-dimensional memristive Hindmarsh–Rose (HR) neuron model is presented in this paper to describe complex dynamics of neuronal activities with electromagnetic induction. The proposed memristive HR neuron model has no equilibrium point but can show hidden dynamical behaviors of coexisting asymmetric attractors, which has not been reported in the previous references for the HR neuron model. Mathematical model based numerical simulations for hidden coexisting asymmetric attractors are performed by bifurcation analyses, phase portraits, attraction basins, and dynamical maps, which just demonstrate the occurrence of complex dynamical behaviors of electrical activities in neuron with electromagnetic induction. Additionally, circuit breadboard based experimental results well confirm the numerical simulations.

scholarly journals A Discrete Huber-braun Neuron Model: From Nodal Properties to Network Performance

2021 ◽  
Author(s):  
Shaoba He ◽  
Karthikeyan Rajagopal ◽  
Anitha Karthikeyan ◽  
Ashokkumar Sriniva
Keyword(s):  
Wave Propagation ◽  
Network Performance ◽  
Neuron Model ◽  
Coupling Effect ◽  
Single Layer ◽  
Simple Wave ◽  
Spiral Waves ◽  
Neuron Models ◽  
Positive Role ◽  
Multiple Wave

Abstract Many of the well-known neuron models are continuous time systems with complex mathematical definitions. Literatures have shown that a discrete mathematical model can effectively replicate the complete dynamical behaviour of a neuron with much reduced complexity. Hence, we propose a new discrete neuron model derived from the Huber-Braun neuron with two additional slow and subthreshold currents alongside the ion channel currents. We have also introduced temperature dependent ion channels to study its effects on the firing pattern of the neuron. With bifurcation and Lyapunov exponents we showed the chaotic and periodic regions of the discrete model. Further to study the complexity of the neuron model, we have used the sample entropy algorithm. Though the individual neuron analysis gives us an idea about the dynamical properties, it’s the collective behaviour which decides the overall behavioural pattern of the neuron. Hence, we investigate the spatiotemporal behaviour of the discrete neuron model in single- and two-layer network. We have considered noise and obstacles as the two important factor which changes the excitability of the neurons in the network. When there is no noise or obstacle, the network display simple wave propagation with highly excitable neurons. Literatures have shown that spiral waves can play a positive role in breaking through quiescent areas of the brain as a pacemaker by creating a coherence resonance behaviour. Hence, we are interested in studying the induced spiral waves in the network. In this condition when an obstacle is introduced the wave propagation is disturbed and we could see multiple wave re-entry and spiral waves. Now when we consider only noise with no obstacle, for selected noise variances the network supports wave re-entry. By introducing an obstacle in this noisy network, the re-entry soon disappears, and the network soon enters idle state with no resetting. In a two-layer network when the obstacle is considered only in one layer and stimulus applied to the layer having the obstacle, the wave re-entry is seen in both the layer though the other layer is not exposed to obstacle. But when both the layers are inserted with an obstacle and stimuli also applied to the layers, they behave like independent layers with no coupling effect. This in a two-layer network stimulus play an important role in spatiotemporal dynamics of the network. Similar noise effects like the single layer network are also seen in the two-layer network.

scholarly journals Dynamical analysis of hollow-shaft dual-rotor system with circular cracks

2020 ◽  
pp. 146134842094828
Author(s):  
Yang Yongfeng ◽  
Wang Jianjun ◽  
Wang Yanlin ◽  
Fu Chao ◽  
Zheng Qingyang ◽  
...  
Keyword(s):  
Critical Speed ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Circular Crack ◽  
Rotor System ◽  
Resonance Phenomenon ◽  
Dynamical Analysis ◽  
Dynamical Response ◽  
Critical Speeds ◽  
Hollow Shaft

In this paper, we considered a dual-rotor system with crack in shaft. The influence of circular crack in hollow shaft on dynamical response was studied. The equations of motion of 12 elements dual-rotor system model were derived. Harmonic balance method was employed to solve the equations. The critical speed and sub-critical speed responses were investigated. It was found that the circular crack in hollow shaft had greater influence on the first-backward critical speed than the first-forward critical speed. Owing to the influence of crack, the vibration peaks occurred at the 1/2, 1/3 and 1/4 critical speeds of the rotor system, along with a reduction in sub-critical speeds and critical speeds. The deeper crack away from the bearing affected the rotor more significantly. The whirling orbits, the time-domain responses and the spectra were obtained to show the super-harmonic resonance phenomenon in hollow-shaft cracked rotor system.

scholarly journals Modulation of Astrocytes on Mode Selection of Neuron Firing Driven by Electromagnetic Induction

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Zhongquan Gao ◽  
Zhixuan Yuan ◽  
Zuo Wang ◽  
Peihua Feng
Keyword(s):  
Membrane Potential ◽  
Resting State ◽  
Electromagnetic Induction ◽  
Neuron Model ◽  
Mode Selection ◽  
Neuron Firing ◽  
Two Factors ◽  
Selection Of ◽  
Strong Ability

Both of astrocytes and electromagnetic induction are magnificent to modulate neuron firing by introducing feedback currents to membrane potential. An improved astro-neuron model considering both of the two factors is employed to investigate their different roles in modulation. The mixing mode, defined by combination of period bursting and depolarization blockage, characterizes the effect of astrocytes. Mixing mode and period bursting alternatively appear in parameter space with respect to the amplitude of feedback current on neuron from astrocyte modulation. However, magnetic flux obviously plays a role of neuron firing inhibition. It not only repels the mixing mode but also suppresses period bursting. The mixing mode becomes period bursting mode and even resting state when astrocytes are hyperexcitable. Abnormal activities of astrocytes are capable to induce depolarization blockage to compose the mixing mode together with bursting mode. But electromagnetic induction shows its strong ability of inhibition of neuron firing, which is also illustrated in the bifurcation diagram. Indeed, the combination of the two factors and appropriate choice of parameters show the great potential to control disorder of neuron firing like epilepsy.

HYPERBOLIC PLYKIN ATTRACTOR CAN EXIST IN NEURON MODELS

2005 ◽  
Vol 15 (11) ◽  
pp. 3567-3578 ◽  
Author(s):  
VLADIMIR BELYKH ◽  
IGOR BELYKH ◽  
ERIK MOSEKILDE
Keyword(s):  
Neuron Model ◽  
Three Dimensional ◽  
Geometrical Approach ◽  
Hyperbolic Attractor ◽  
Neuron Models ◽  
Neuron System ◽  
Physical Systems ◽  
System A ◽  
Bursting Neurons ◽  
Hyperbolic Attractors

Strange hyperbolic attractors are hard to find in real physical systems. This paper provides the first example of a realistic system, a canonical three-dimensional (3D) model of bursting neurons, that is likely to have a strange hyperbolic attractor. Using a geometrical approach to the study of the neuron model, we derive a flow-defined Poincaré map giving an accurate account of the system's dynamics. In a parameter region where the neuron system undergoes bifurcations causing transitions between tonic spiking and bursting, this two-dimensional map becomes a map of a disk with several periodic holes. A particular case is the map of a disk with three holes, matching the Plykin example of a planar hyperbolic attractor. The corresponding attractor of the 3D neuron model appears to be hyperbolic (this property is not verified in the present paper) and arises as a result of a two-loop (secondary) homoclinic bifurcation of a saddle. This type of bifurcation, and the complex behavior it can produce, have not been previously examined.

Bifurcations of Negative Responses to Positive Feedback Current Mediated by Memristor in a Neuron Model with Bursting Patterns

2020 ◽  
Vol 30 (04) ◽  
pp. 2030009 ◽  
Author(s):  
Fuqiang Wu ◽  
Huaguang Gu
Keyword(s):  
Bifurcation Point ◽  
Positive Feedback ◽  
Electromagnetic Induction ◽  
Neuron Model ◽  
Firing Frequency ◽  
Feedback Gain ◽  
Induction Effect ◽  
Nonlinear Phenomenon ◽  
Neural Firing ◽  
Dynamical Mechanism

In contrast to traditional viewpoint that positive feedback current always enhances neural firing activities, in the present paper, we identify that the excitatory feedback current mediated by memristor can induce negative responses of bursting patterns, which can be well interpreted with bifurcations. For the Hindmarsh–Rose neuron model without memristor, the period-adding bifurcations of bursting patterns and increase of firing frequency can be induced by increasing the excitatory effect of the background current. After introducing a memristor to simulate the biological synapse or electromagnetic induction effect, inverse period-adding or complex bifurcations of bursting patterns are induced by the excitatory feedback current mediated by the memristor. The number of spikes per burst becomes smaller and the firing frequency becomes lower when increasing the positive feedback gain. Such negative responses of bursting patterns to the positive feedback current are demonstrated in a circuit designed with Digital Signal Processor systems of the MatLab software. Furthermore, the underlying bifurcation mechanism of the negative responses to the positive feedback is acquired with fast–slow variable dissection method. With increasing feedback gain, the initial phase of the burst, which corresponds to a saddle-node bifurcation point of the fast subsystem, delays, while the termination phase of the burst, which corresponds to a saddle-homoclinic bifurcation point, remains unchanged. Therefore, the burst becomes narrower with increasing feedback gain, which leads to decrease in the number of spikes within a burst and decrease in firing frequency. The results present a paradoxical nonlinear phenomenon and the dynamical mechanism, which is helpful for understanding the functions of memristor and roles of the electromagnetic induction current.

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