scholarly journals Firing Activities in Fractional-Order Hindmarsh-Rose Neuron with Multistable Memristor as Autapse

2021 ◽  
Author(s):  
Zhijun Li ◽  
WenQiang Xie ◽  
Jinfang Zeng ◽  
Yicheng Zeng
Keyword(s):  
Fractional Order ◽  
Neuron Model ◽  
Hysteresis Loops ◽  
Active Regions ◽  
Firing Frequency ◽  
Initial Value ◽  
Firing Patterns ◽  
Firing Behavior ◽  
Order Neuron ◽  
Current Coupling

Abstract Compared with integer order neurons, fractional-order neuron model can more accurately describe the firing behavior of biological neurons. Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is firstly proposed in this study. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of HR neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional order on the firing behavior are discussed by time series, phase diagrams, Lyapunov exponents and inter spike interval (ISI) bifurcation diagrams. Three coexisting firing patterns, including irregulate A-periodic bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values are observed. It is also revealed that the fractional order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional order is designed to verify the numerical simulations.

scholarly journals Multiple Firing Patterns in Coupled Hindmarsh-Rose Neurons with a Nonsmooth Memristor

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xuerong Shi ◽  
Zuolei Wang
Keyword(s):  
Qualitative Analysis ◽  
Neuron Model ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
External Forcing ◽  
Coupling Coefficients ◽  
Initial Value ◽  
Firing Patterns ◽  
Stability Of Equilibrium ◽  
The Stability

A model is introduced by coupling two three-dimensional Hindmarsh-Rose models with the help of a nonsmooth memristor. The firing patterns dependent on the external forcing current are explored, which undergo a process from adding-period to chaos. The stability of equilibrium points of the considered model is investigated via qualitative analysis, from which it can be gained that the model has diversity in the number and stability of equilibrium points for different coupling coefficients. The coexistence of multiple firing patterns relative to initial values is revealed, which means that the referred model can appear various firing patterns with the change of the initial value. Multiple firing patterns of the addressed neuron model induced by different scales are uncovered, which suggests that the discussed model has a multiscale effect for the nonzero initial value.

scholarly journals Vibrational Resonance and Electrical Activity Behavior of a Fractional-Order FitzHugh–Nagumo Neuron System

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 87
Author(s):  
Jia-Wei Mao ◽  
Dong-Liang Hu
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Neuron Model ◽  
Low Frequency ◽  
Order Model ◽  
Vibrational Resonance ◽  
Frequency Signal ◽  
Neuron System ◽  
Order Neuron ◽  
Activity Behavior

Making use of the numerical simulation method, the phenomenon of vibrational resonance and electrical activity behavior of a fractional-order FitzHugh–Nagumo neuron system excited by two-frequency periodic signals are investigated. Based on the definition and properties of the Caputo fractional derivative, the fractional L1 algorithm is applied to numerically simulate the phenomenon of vibrational resonance in the neuron system. Compared with the integer-order neuron model, the fractional-order neuron model can relax the requirement for the amplitude of the high-frequency signal and induce the phenomenon of vibrational resonance by selecting the appropriate fractional exponent. By introducing the time-delay feedback, it can be found that the vibrational resonance will occur with periods in the fractional-order neuron system, i.e., the amplitude of the low-frequency response periodically changes with the time-delay feedback. The weak low-frequency signal in the system can be significantly enhanced by selecting the appropriate time-delay parameter and the fractional exponent. In addition, the original integer-order model is extended to the fractional-order model, and the neuron system will exhibit rich dynamical behaviors, which provide a broader understanding of the neuron system.

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 fractional-order multistable locally-active memristor and its chaotic system with transient transition, state jump

2021 ◽  
Author(s):  
Xie Wenli ◽  
Chunhua Wang ◽  
Lin Hairong
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Chaotic Oscillation ◽  
Hysteresis Loops ◽  
Active Regions ◽  
Period 2 ◽  
Theoretical And Numerical Analysis ◽  
Memory Characteristics

Abstract Fractional calculus is closer to reality and has the same memory characteristics as memristor. Therefore, a fractional-order multistable locally active memristor is proposed for the first time in this paper, which has infinitely many coexisting pinched hysteresis loops under different initial states and wide locally active regions. Through the theoretical and numerical analysis, it is found that the fractional-order memristor has stronger locally active and memory characteristics and wider nonvolatile ranges than the integer-order memristor. Furthermore, this fractional-order memristor is applied in a chaotic system. It is found that oscillations occur only within the locally active regions. This chaotic system not only has complex and rich nonlinear dynamics such as infinitely many discrete equilibrium points, multistability, anti-monotonicity but also produces two new phenomena that have not been found in other chaotic systems after neglecting some initial transients. The first one is transient transition: the behavior of transient chaotic and transient period transition alternately occurring. The second is state jump: the behavior of period-4 oscillation or chaotic oscillation jumping to period-2 oscillation.Finally, the circuit simulation of fractional-order multistable locally active memristive chaotic system using PSIM is carried out to verify the validity of the numerical simulation results.

scholarly journals Firing responses mediated via distinct nicotinic acetylcholine receptor subtypes in rat prepositus hypoglossi nuclei neurons

2018 ◽  
Vol 120 (4) ◽  
pp. 1525-1533
Author(s):  
Yue Zhang ◽  
Yuchio Yanagawa ◽  
Yasuhiko Saito
Keyword(s):  
Acetylcholine Receptor ◽  
Nicotinic Acetylcholine Receptor ◽  
Firing Frequency ◽  
Membrane Properties ◽  
Receptor Subtypes ◽  
Nicotinic Acetylcholine ◽  
Firing Patterns ◽  
Prepositus Hypoglossi ◽  
Specific Antagonist ◽  
The Relationship

We previously reported that cholinergic current responses mediated via nicotinic acetylcholine (ACh) receptors (nAChRs) in the prepositus hypoglossi nucleus (PHN), which participates in gaze control, can be classified into distinct types based on different kinetics and are mainly composed of α7- and/or non-α7-subtypes: fast (F)-, slow (S)-, and fast and slow (FS)-type currents. In this study, to clarify how each current type is related to neuronal activities, we investigated the relationship between the current types and the membrane properties and the firing responses that were induced by each current type. The proportion of the current types differed in neurons that exhibited different afterhyperpolarization (AHP) profiles and firing patterns, suggesting that PHN neurons show a preference for specific current types dependent on the membrane properties. In response to ACh, F-type neurons showed either one action potential (AP) or multiple APs with a short firing duration, and S-type neurons showed multiple APs with a long firing duration. The firing frequency of F-type neurons was significantly higher than that of S-type and FS-type neurons. An α7-subtype-specific antagonist abolished the firing responses of F-type neurons and reduced the responses of FS-type neurons but had little effect on the responses of S-type neurons, which were reduced by a non-α7-subtype-specific antagonist. These results suggest that the different properties of the current types and the distinct expression of the nAChR subtypes in PHN neurons with different membrane properties produce unique firing responses via the activation of nAChRs. NEW & NOTEWORTHY Prepositus hypoglossi nucleus (PHN) neurons show distinct nicotinic acetylcholine receptor (nAChR)-mediated current responses. The proportion of the current types differed in the neurons that exhibited different afterhyperpolarization profiles and firing patterns. The nAChR-mediated currents with different kinetics induced firing responses of the neurons that were distinct in the firing frequency and duration. These results suggest that the different properties of the current types in PHN neurons with different membrane properties produce unique firing responses via the activation of nAChRs.

Low-Voltage Low-Power Integrable CMOS Circuit Implementation of Integer- and Fractional–Order FitzHugh–Nagumo Neuron Model

2019 ◽  
Vol 30 (7) ◽  
pp. 2108-2122 ◽  
Author(s):  
Farooq Ahmad Khanday ◽  
Nasir Ali Kant ◽  
Mohammad Rafiq Dar ◽  
Tun Zainal Azni Zulkifli ◽  
Costas Psychalinos
Keyword(s):  
Low Power ◽  
Fractional Order ◽  
Neuron Model ◽  
Low Voltage ◽  
Cmos Circuit ◽  
Circuit Implementation

scholarly journals Fractional order differential inclusions on an unbounded domain with infinite delay

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 167-178
Author(s):  
Mohamed Helal
Keyword(s):  
Fractional Order ◽  
Initial Value Problems ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Fréchet Spaces ◽  
Initial Value ◽  
Nonlinear Alternative ◽  
Hyperbolic Differential Inclusions

We provide sufficient conditions for the existence of solutions to initial value problems, for partial hyperbolic differential inclusions of fractional order involving Caputo fractional derivative with infinite delay by applying the nonlinear alternative of Frigon type for multivalued admissible contraction in Frechet spaces.

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