Memristors-coupled neuron models with multiple firing patterns and homogeneous and heterogeneous multistability

Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for neurons.In this paper,two distinct scenarios,i.e.,an ideal memristor serves as external electromagnetic stimulation and a locally active memristor serves as a synapse,are formulated to investigate the impact of a memristor on a two-dimensional Hindmarsh-Rose neuron model.Numerical simulations show that the neuronal models in different scenarios have multiple burst firing patterns.The introduction of the memristor makes the neuronal model exhibit complex dynamical behaviors.Finally,the simulation circuit and DSP hardware implementation results validate the physical mechanism,as well as the reliability of the biological neuron model.

Noise-Induced Transition in a Voltage-Controlled Oscillator Neuron Model

In the presence of Gaussian white noise,we study the properties of voltage-controlled oscillator neuronmodel and discuss the effects of the additive and multiplicative noise.It is found that the additive noise can accelerate andcounterwork the firing of neuron,which depends on the value of central frequency of neuron itself,while multiplicativenoise can induce the continuous change or mutation of membrane potential.

Fixed Point Theorem and Fractional Differential Equations with Multiple Delays Related with Chaos Neuron Models

In this paper, we show a fixed point theorem which deduces to both of Lou’s fixed point theorem and de Pascale and de Pascale’s fixed point theorem. Moreover, our result can be applied to show the existence and uniqueness of solutions for fractional differential equations with multiple delays. Using the theorem, we discuss the fractional chaos neuron model.

A New Kind of Artificial Neuron Models

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Advances in memristor based artificial neuron fabrication-materials,models,and applications

Spiking neural network(SNN),widely known as the third-generation neural network,has been frequently investigated due to its excellent spatiotemporal information processing capability,high biological plausibility,and low energy consumption characteristics.Analogous to the working mechanism of human brain,the SNN system transmits information through the spiking action of neurons.Therefore,artificial neurons are critical building blocks for constructing SNN in hardware.Memristors are drawing growing attention due to low consumption,high speed,and nonlinearity characteristics,which are recently introduced to mimic the functions of biological neurons.Researchers have proposed multifarious memristive materials including organic materials,inorganic materials,or even two-dimensional materials.Taking advantage of the unique electrical behavior of these materials,several neuron models are successfully implemented,such as Hodgkin–Huxley model,leaky integrate-and-fire model and integrate-and-fire model.In this review,the recent reports of artificial neurons based on memristive devices are discussed.In addition,we highlight the models and applications through combining artificial neuronal devices with sensors or other electronic devices.Finally,the future challenges and outlooks of memristor-based artificial neurons are discussed,and the development of hardware implementation of brain-like intelligence system based on SNN is also prospected.

A neuron model with trainable activation function (TAF) and its MFNN supervised learning

This paper addresses a new kind of neuron model, which has trainable activation function (TAF) in addition to only trainable weights in the conventional M-P model. The final neuron activation function can be derived from a primitive neuron activation function by training. The BP like learning al-gorithm has been presented for MFNN constructed by neurons of TAP model. Several simulation ex-amples are given to show the network capacity and performance advantages of the new MFNN in com-parison with that of conventional sigmoid MFNN.

Discrete memristive neuron model and its interspike interval-encoded application in image encryption

Bursting is a diverse and common phenomenon in neuronal activation patterns and it indicates that fast action voltage spiking periods are followed by resting periods.The interspike interval(ISI)is the time between successive action voltage spikes of neuron and it is a key indicator used to characterize the bursting.Recently,a three-dimensional memristive Hindmarsh-Rose(mHR)neuron model was constructed to generate hidden chaotic bursting.However,the properties of the discrete mHR neuron model have not been investigated,yet.In this article,we first construct a discrete mHR neuron model and then acquire different hidden chaotic bursting sequences under four typical sets of parameters.To make these sequences more suitable for the application,we further encode these hidden chaotic sequences using their ISIs and the performance comparative results show that the ISI-encoded chaotic sequences have much more complex chaos properties than the original sequences.In addition,we apply these ISI-encoded chaotic sequences to the application of image encryption.The image encryption scheme has a symmetric key structure and contains plain-text permutation and bidirectional diffusion processes.Experimental results and security analyses prove that it has excellent robustness against various possible attacks.

A new photosensitive neuron model and its dynamics

Biological neurons can receive inputs and capture a variety of external stimuli,which can be encoded and transmitted as different electric signals.Thus,the membrane potential is adjusted to activate the appropriate firing modes.Indeed,reliable neuron models should take intrinsic biophysical effects and functional encoding into consideration.One fascinating and important question is the physical mechanism for the transcription of external signals.External signals can be transmitted as a transmembrane current or a signal voltage for generating action potentials.We present a photosensitive neuron model to estimate the nonlinear encoding and responses of neurons driven by external optical signals.In the model,a photocell(phototube)is used to activate a simple FitzHugh-Nagumo(FHN)neuron,and then external optical signals(illumination)are imposed to excite the photocell for generating a time-varying current/voltage source.The photocell-coupled FHN neuron can therefore capture and encode external optical signals,similar to artificial eyes.We also present detailed bifurcation analysis for estimating the mode transition and firing pattern selection of neuronal electrical activities.The sampled time series can reproduce the main characteristics of biological neurons(quiescent,spiking,bursting,and even chaotic behaviors)by activating the photocell in the neural circuit.These results could be helpful in giving possible guidance for studying neurodynamics and applying neural circuits to detect optical signals.

Memristive effects on an improved discrete Rulkov neuron model

A change in neuronal-action potential can generate a magnetically induced current during the release and propagation of intracellular ions.To better characterize the electromagnetic-induction effect,this paper presents an improved discrete Rulkov(ID-Rulkov)neuron model by coupling a discrete model of a memristor with sine memductance into a discrete Rulkov neuron model.The ID-Rulkov neuron model possesses infinite invariant points,and its memristor-induced stability effect is evaluated by detecting the routes of period-doubling and Neimark-Sacker bifurcations.We investigated the memristor-induced dynamic effects on the neuron model using bifurcation plots and firing patterns.Meanwhile,we theoretically expounded the memristor initial-boosting mechanism of infinite coexisting patterns.The results show that the ID-Rulkov neuron model can realize diverse neuron firing patterns and produce hyperchaotic attractors that are nondestructively boosted by the initial value of the memristor,indicating that the introduced memristor greatly benefits the original neuron model.The hyperchaotic attractors initially boosted by the memristor were verified by hardware experiments based on a hardware platform.In addition,pseudorandom number generators are designed using the ID-Rulkov neuron model,and their high randomness is demonstrated based onstrict test results.

Memristive neuron model with an adapting synapse and its hardware experiments

Electromagnetic induction effect caused by neuron potential can be mimicked using memristor.This paper considers a fluxcontrolled memristor to imitate the electromagnetic induction effect of adapting feedback synapse and presents a memristive neuron model with the adapting synapse.The memristive neuron model is three-dimensional and non-autonomous.It has the time-varying equilibria with multiple stabilities,which results in the global coexistence of multiple firing patterns.Multiple numerical plots are executed to uncover diverse coexisting firing patterns in the memristive neuron model.Particularly,a nonlinear fitting scheme is raised and a fitting activation function circuit is employed to implement the memristive mono-neuron model.Diverse coexisting firing patterns are observed from the hardware experiment circuit and the measured results verify the numerical simulations well.

Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay

The firing of a neuron model is mainly affected by the following factors:the magnetic field,external forcing current,time delay,etc.In this paper,a new time-delayed electromagnetic field coupled dual Hindmarsh-Rose neuron network model is constructed.A magnetically controlled threshold memristor is improved to represent the self-connected and the coupled magnetic fields triggered by the dynamic change of neuronal membrane potential for the adjacent neurons.Numerical simulation confirms that the coupled magnetic field can activate resting neurons to generate rich firing patterns,such as spiking firings,bursting firings,and chaotic firings,and enable neurons to generate larger firing amplitudes.The study also found that the strength of magnetic coupling in the neural network also affects the number of peaks in the discharge of bursting firing.Based on the existing medical treatment background of mental illness,the effects of time lag in the coupling process against neuron firing are studied.The results confirm that the neurons can respond well to external stimuli and coupled magnetic field with appropriate time delay,and keep periodic firing under a wide range of external forcing current.

DYNAMICS IN A CLASS OF NEURON MODELS

In this paper, we investigate the dynamics in a class of discrete-time neuron mod-els. The neuron model we discussed, defined by such periodic input-output mapping as a sinusoidal function, has a remarkably larger memory capacity than the conven-tional association system with the monotonous function. Our results show that the orbit of the model takes a conventional bifurcation route, from stable equilibrium, to periodicity, even to chaotic region. And the theoretical analysis is verified by numerical simula...

STABILITY ANALYSIS OF H-R NEURON MODEL WITH FRACTIONAL ORDERS

In this paper,we are concerned with a Hindmarsh-Rose(H-R) neuron model of fractional orders.By employing stability theory,we present some sufficient conditions ensuring the equilibrium of system to be stable.The simulations are provided to verify the theoretical results.

Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses

The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.

Using induced pluripotent stem cells derived neurons to model brain diseases

The ability to use induced pluripotent stem cells（i PSC）to model brain diseases is a powerful tool for unraveling mechanistic alterations in these disorders.Rodent models of brain diseases have spurred understanding of pathology but the concern arises that they may not recapitulate the full spectrum of neuron disruptions associated with human neuropathology.iPSC derived neurons,or other neural cell types,provide the ability to access pathology in cells derived directly from a patient＇s blood sample or skin biopsy where availability of brain tissue is limiting.Thus,utilization of iPSC to study brain diseases provides an unlimited resource for disease modelling but may also be used for drug screening for effective therapies and may potentially be used to regenerate aged or damaged cells in the future.Many brain diseases across the spectrum of neurodevelopment,neurodegenerative and neuropsychiatric are being approached by iPSC models.The goal of an iPSC based disease model is to identify a cellular phenotype that discriminates the disease-bearing cells from the control cells.In this mini-review,the importance of iPSC cell models validated for pluripotency,germline competency and function assessments is discussed.Selected examples for the variety of brain diseases that are being approached by iPSC technology to discover or establish the molecular basis of the neuropathology are discussed.

Determinants of Response Pattern of Cochlear Nucleus Neuron:a Study Based on the Model

Objective: Neurons in the cochlear nucleus show different response patterns to the short tone bursts. Because of the limitations of animal experiments, it is hard to explore the principle. Therefore, using a model to simulate CN neurons will be a feasible way. Methods: Based on the initial model mentioned in the previous study, we proposed an improved CN model in MATLAB R2012b. Results: By modifying the parameters of the model we found the interchanges among "primary-like", "chopper",and "onset" response patterns. Furthermore, we simulated the "pauser" response pattern by adding an extra input in our model. Conclusion: The results indicate that the synaptic integrations and the input modes can give rise to different characteristics of CN neurons, which eventually determine the response patterns of CN neurons.

Dynamics and synchronization of neural models with memristive membranes under energy coupling

Dynamical modeling of neural systems plays an important role in explaining and predicting some features of biophysical mechanisms.The electrophysiological environment inside and outside of the nerve cell is different.Due to the continuous and periodical properties of electromagnetic fields in the cell during its operation,electronic components involving two capacitors and a memristor are effective in mimicking these physical features.In this paper,a neural circuit is reconstructed by two capacitors connected by a memristor with periodical mem-conductance.It is found that the memristive neural circuit can present abundant firing patterns without stimulus.The Hamilton energy function is deduced using the Helmholtz theorem.Further,a neuronal network consisting of memristive neurons is proposed by introducing energy coupling.The controllability and flexibility of parameters give the model the ability to describe the dynamics and synchronization behavior of the system.

From neurogenesis to neuronal regeneration: the amphibian olfactory system as a model to visualize neuronal development in vivo

How do individual neurons develop and how are they in- tegrated into neuronal circuitry？ To answer this question is essential to understand how the nervous system develops and how it is maintained during the adult life. A neural stem cell must go through several stages of maturation, including proliferation, migration, differentiation, and integration, to become fully embedded to an existing neuronal circuit. The knowledge on this topic so far has come mainly from cell culture studies. Studying the development of individual neurons within intact neuronal networks in vivo is inherently difficult. Most neurons are generated form neural stem cells during embryonic and early postnatal development.

Numerical Simulation Analysis of a Mathematical Model of Circadian Pacemaker Neurons

Sim and Forger have proposed a mathematical model of circadian pacemaker neurons in the suprachiasmatic nucleus (SCN). This model, which has been formulated on the Hodgkin-Huxley mo-del, is described by a system of nonlinear ordinary differential equations. An important feature of the SCN neurons observed in electrophysiological recording is spontaneous repetitive spiking, which is reproduced using this model. In the present study, numerical simulation analysis of this model was performed to evaluate variations in two system parameters of this model: the maximal conductance of calcium current (gCa) and the maximal conductance of sodium current (gNa). Simulation results revealed the spontaneous repetitive spiking states of the model in the (gCa, gNa)-pa-rameter space.