Dynamic expression of a HR neuron model under an electric field

2020 ◽  
pp. 2150024
Author(s):  
Shuai Qiao ◽  
Xin-Lei An
Keyword(s):  
Electric Field ◽  
Neuron Model ◽  
Basins Of Attraction ◽  
Firing Activity ◽  
Complex Dynamic ◽  
Oscillation Pattern ◽  
Dynamic Expression ◽  
Subcritical Hopf Bifurcation ◽  
Oscillation Modes ◽  
Discharge Behavior

The movement of large amounts of ions (e.g., potassium, sodium and calcium) in the nervous system triggers time-varying electromagnetic fields that further regulate the firing activity of neurons. Accordingly, the discharge states of a modified Hindmarsh–Rose (HR) neuron model under an electric field are studied by numerical simulation. By using the Matcont software package and its programming, the global basins of attraction for the model are analyzed, and it is found that the model has a coexistence oscillation pattern and hidden discharge behavior caused by subcritical Hopf bifurcation. Furthermore, the model’s unstable branches are effectively controlled based on the Washout controller and eliminating the hidden discharge states. Interestingly, by analyzing the two-parametric bifurcation analysis, we also find that the model generally has a comb-shaped chaotic structure and a periodic-adding bifurcation pattern. Additionally, considering that the electric field is inevitably disturbed periodically, the discharge states of this model are more complex and have abundant coexisting oscillation modes. The research results will provide a useful reference for understanding the complex dynamic characteristics of neurons under an electric field.

scholarly journals Нелинейная динамика паттернов импульсной активности ноцицептивных нейронов при коррекции повреждающего болевого воздействия

2019 ◽  
Vol 89 (3) ◽  
pp. 465
Author(s):  
О.Е. Дик
Keyword(s):  
Bifurcation Analysis ◽  
Active Ingredient ◽  
Activity Pattern ◽  
Neuron Model ◽  
Nociceptive Neuron ◽  
Firing Activity ◽  
Comenic Acid ◽  
Pain Stimulation ◽  
Activation Gating ◽  
Nonopioid Analgesic

AbstractA bifurcation analysis of a nociceptive neuron model was performed to study how the firing activity pattern changes when an antinociceptive response to damaging pain stimulation arises in rat dorsal ganglia. Ectopic train activity was found to arise in the model. Suppression of train activity was demonstrated to proceed solely through modification of the activation gating structure of the Na _ V 1.8 slow sodium channel in response to comenic acid, which exerts an analgesic effect and is an active ingredient of the new nonopioid analgesic Anoceptin.

Modified Morris-Lecar neuron model: Effects of very low frequency electric fields and of magnetic fields on the local and network dynamics of an excitable media

2021 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Irene Moroz ◽  
Balamurali Ramakrishnan ◽  
Anitha Karthikeyan ◽  
Prakash Duraisamy
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Field ◽  
Neuron Model ◽  
Low Noise ◽  
Spiral Waves ◽  
Excitable Media ◽  
Field Frequency ◽  
Electric And Magnetic Fields ◽  
Electric Field Frequency

Abstract A Morris-Lecar neuron model is considered with Electric and Magnetic field effects where the electric field is a time varying sinusoid and magnetic field is simulated using an exponential flux memristor. We have shown that the exposure to electric and magnetic fields have significant effects on the neurons and have exhibited complex oscillations. The neurons exhibit a frequency-locked state for the periodic electric field and different ratios of frequency locked states with respect to the electric field frequency is also presented. To show the impact of the electric and magnetic fields on network of neurons, we have constructed different types of network and have shown the network wave propagation phenomenon. Interestingly the nodes exposed to both electric and magnetic fields exhibit more stable spiral waves compared to the nodes exhibited only to the magnetic fields. Also, when the number of layers are increased the range of electric field frequency for which the layers exhibit spiral waves also increase. Finally the noise effects on the field affected neuron network are discussed and multilayer networks supress spiral waves for a very low noise variance compared against the single layer network.

CHARACTERIZATION OF CHAOTIC ATTRACTORS INSIDE BAND-MERGING SCENARIO IN A ZAD-CONTROLLED BUCK CONVERTER

2012 ◽  
Vol 22 (10) ◽  
pp. 1230034
Author(s):  
JOHN ALEXANDER TABORDA ◽  
FABIOLA ANGULO ◽  
GERARD OLIVAR
Keyword(s):  
Control Strategy ◽  
Control Parameter ◽  
Period Doubling ◽  
Basins Of Attraction ◽  
Buck Converter ◽  
Chaotic Attractors ◽  
Complex Dynamic ◽  
Self Similar ◽  
Dynamic Links

Zero Average Dynamics (ZAD) control strategy has been developed, applied and widely analyzed in the last decade. Numerous and interesting phenomena have been studied in systems controlled by ZAD strategy. In particular, the ZAD-controlled buck converter has been a source of nonlinear and nonsmooth phenomena, such as period-doubling, merging bands, period-doubling bands, torus destruction, fractal basins of attraction or codimension-2 bifurcations. In this paper, we report a new bifurcation scenario found inside band-merging scenario of ZAD-controlled buck converter. We use a novel qualitative framework named Dynamic Linkcounter (DLC) approach to characterize chaotic attractors between consecutive crisis bifurcations. This approach complements the results that can be obtained with Bandcounter approaches. Self-similar substructures denoted as Complex Dynamic Links (CDLs) are distinguished in multiband chaotic attractors. Geometrical changes in multiband chaotic attractors are detected when the control parameter of ZAD strategy is varied between two consecutive crisis bifurcations. Linkcount subtracting staircases are defined inside band-merging scenario.

A Cybernetic Approach for Modelling of Complex Dynamic Expression in Recombinant Protein Production with Pichia pastoris

2010 ◽  
Vol 43 (6) ◽  
pp. 383-388
Author(s):  
Reiner Luttmann ◽  
Elisabeth Hukelmann ◽  
Andree Ellert ◽  
Ali Kazemi ◽  
Gesine Cornelissen
Keyword(s):  
Pichia Pastoris ◽  
Recombinant Protein ◽  
Recombinant Protein Production ◽  
Protein Production ◽  
Complex Dynamic ◽  
Dynamic Expression

scholarly journals Action potential initial dynamical mechanism analysis in a minimum neuron model exposure to TMS induced electric field

2012 ◽  
Vol 61 (11) ◽  
pp. 118701
Author(s):  
Jin Qi-Tao ◽  
Wang Jiang ◽  
Yi Guo-Sheng ◽  
Li Hui-Yan ◽  
Deng Bin ◽  
...  
Keyword(s):  
Electric Field ◽  
Action Potential ◽  
Neuron Model ◽  
Mechanism Analysis ◽  
Dynamical Mechanism

scholarly journals Self-Evolutionary Neuron Model for Fast-Response Spiking Neural Networks

2022 ◽  
Author(s):  
Anguo Zhang ◽  
Ying Han ◽  
Jing Hu ◽  
Yuzhen Niu ◽  
Yueming Gao ◽  
...  
Keyword(s):  
Neuron Model ◽  
Response Speed ◽  
Fast Response ◽  
Spiking Neural Networks ◽  
Spiking Neural Network ◽  
Spiking Neuron ◽  
Firing Activity ◽  
Neuron Models ◽  
Spiking Neuron Models ◽  
Classification Tasks

We propose two simple and effective spiking neuron models to improve the response time of the conventional spiking neural network. The proposed neuron models adaptively tune the presynaptic input current depending on the input received from its presynapses and subsequent neuron firing events. We analyze and derive the firing activity homeostatic convergence of the proposed models. We experimentally verify and compare the models on MNIST handwritten digits and FashionMNIST classification tasks. We show that the proposed neuron models significantly increase the response speed to the input signal.

DYNAMIC COMPLEXITIES IN AN EPIDEMIC MODEL WITH BIRTH PULSES AND PULSE CULLING

2007 ◽  
Vol 17 (02) ◽  
pp. 521-533 ◽  
Author(s):  
SHUJING GAO ◽  
LANSUN CHEN ◽  
ZHIDONG TENG ◽  
DEHUI XIE
Keyword(s):  
Birth Rate ◽  
Discrete Dynamical System ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
Basins Of Attraction ◽  
Complex Dynamic ◽  
Natural Period ◽  
Dynamical Behaviors ◽  
Threshold Conditions ◽  
Fixed Times

In this paper, we propose a model for the dynamics of a fatal infectious disease in a wild animal population with birth pulses and pulse culling, where periodic birth pulses and pulse culling occur at different fixed times. Using the discrete dynamical system determined by stroboscopic map, we obtain an exact cycle of the system, and obtain the threshold conditions for its stability. Bifurcation diagrams are constructed with the birth rate (or culling effort) as the bifurcation parameter, and these are observed to display complex dynamic behaviors, including chaotic bands with period windows, period-doubling and period-halving bifurcations, pitch-fork and tangent bifurcations, nonunique dynamics (meaning that several attractors or attractor and chaos coexist), basins of attraction and attractor crisis. This suggests that birth pulses and pulse culling provide a natural period or cyclicity that makes the dynamical behaviors more complex. Moreover, we investigate the sufficient conditions for global stability of semi-trivial periodic solutions.

scholarly journals Further Discussions of the Complex Dynamics of a 2D Logistic Map: Basins of Attraction and Fractal Dimensions

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2001
Author(s):  
Sameh S. Askar ◽  
Abdulrahman Al-Khedhairi
Keyword(s):  
Phase Plane ◽  
Complex Dynamics ◽  
Logistic Map ◽  
Fractal Dimensions ◽  
Basins Of Attraction ◽  
Chaotic Attractors ◽  
Complex Dynamic ◽  
2D Logistic Map ◽  
Two Parameters ◽  
Periodic Cycles

In this paper, we study the complex dynamic characteristics of a simple nonlinear logistic map. The map contains two parameters that have complex influences on the map’s dynamics. Assuming different values for those parameters gives rise to strange attractors with fractal dimensions. Furthermore, some of these chaotic attractors have heteroclinic cycles due to saddle-fixed points. The basins of attraction for some periodic cycles in the phase plane are divided into three regions of rank-1 preimages. We analyze those regions and show that the map is noninvertible and includes Z0,Z2 and Z4 regions.

Three-dimensional oscillation characteristics of electrostatically deformed drops

1991 ◽  
Vol 227 ◽  
pp. 429-447 ◽  
Author(s):  
James Q. Feng ◽  
Kenneth V. Beard
Keyword(s):  
Electric Field ◽  
Three Dimensional ◽  
Normal Modes ◽  
Oscillation Mode ◽  
Mode Shapes ◽  
Physical Factors ◽  
Mathematical Framework ◽  
Drop Shape ◽  
Oscillation Modes ◽  
Oscillation Characteristics

A three-dimensional asymptotic analysis of the oscillations of electrically charged drops in an external electric field is carried out by means of the multiple-parameter perturbation method. The mathematical framework allows separate treatments of the quiescent deformation due to the electric field and the oscillatory motions caused by other physical factors. Without oscillations, the solution for the quiescent drop shape exhibits a prolate deformation with a slight asymmetry about the drop's equatorial plane. This axisymmetric quiescent deformation of the equilibrium drop shape is shown to modify the oscillation characteristics of axisymmetric as well as asymmetric modes. The expression of the characteristic frequency modification is derived for the oscillation modes, manifesting fine structure in the frequency spectrum so the degeneracy of Rayleigh's normal modes for charged drops is removed in the presence of an electric field. Physical reasoning indicates that the degeneracy of the oscillation modes is associated with the spherical symmetry of the system, so the removal of the degeneracy may be regarded as a consequence of the symmetry breaking caused by the electric field. In addition, the small-amplitude oscillation mode shapes are also modified as a result of the coupling between the oscillatory motions and the electric field as well as the quiescent deformation.

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