Morris-Lecar Research Articles

Dynamical effects of low-frequency and high-frequency current stimuli in a memristive Morris–Lecar neuron model

This paper deduces that the potassium and calcium ion currents in the two-dimensional (2D) Morris–Lecar neuron model can be respectively characterized by a passive memristor and a locally active memristor. Then a memristive Morris–Lecar neuron model with an equivalent circuit scheme is first constructed. The equilibrium trajectory and its stability are analyzed, which displays fold and Hopf bifurcations with proper model parameters. Bursting behavior and mixed-mode oscillations with after-depolarizing potential for low-frequency current stimulus are numerically disclosed. Besides, the bifurcation mechanisms for bursting behavior and mixed-mode oscillations are theoretically deduced. Furthermore, the firing patterns and antimonotonicity phenomenon for high-frequency current stimulus are numerically discovered. This study provides a new concept for building memristive bionic circuits from neuron models with well-defined ion channel currents.

A Rectified Linear Unit-Based Memristor-Enhanced Morris–Lecar Neuron Model

This paper introduces a modified Morris–Lecar neuron model that incorporates a memristor with a ReLU-based activation function. The impact of the memristor on the dynamics of the ML neuron model is analyzed using bifurcation diagrams and Lyapunov exponents. The findings reveal chaotic behavior within specific parameter ranges, while increased magnetic strength tends to maintain periodic dynamics. The emergence of various firing patterns, including periodic and chaotic spiking as well as square-wave and triangle-wave bursting is also evident. The modified model also demonstrates multistability across certain parameter ranges. Additionally, the dynamics of a network of these modified models are explored. This study shows that synchronization depends on the strength of the magnetic flux, with synchronization occurring at lower coupling strengths as the magnetic flux increases. The network patterns also reveal the formation of different chimera states, such as traveling and non-stationary chimera states.

Deep brain stimulation and lag synchronization in a memristive two-neuron network

In the pursuit of potential treatments for neurological disorders and the alleviation of patient suffering, deep brain stimulation (DBS) has been utilized to intervene or investigate pathological neural activities. To explore the exact mechanism of how DBS works, a memristive two-neuron network considering DBS is newly proposed in this work. This network is implemented by coupling two-dimensional Morris–Lecar neuron models and using a memristor synaptic synapse to mimic synaptic plasticity. The complex bursting activities and dynamical effects are revealed numerically through dynamical analysis. By examining the synchronous behavior, the desynchronization mechanism of the memristor synapse is uncovered. The study demonstrates that synaptic connections lead to the appearance of time-lagged or asynchrony in completely synchronized firing activities. Additionally, the memristive two-neuron network is implemented in hardware based on FPGA, and experimental results confirm the abundant neuronal electrical activities and chaotic dynamical behaviors. This work offers insights into the potential mechanisms of DBS intervention in neural networks.

Weak signal detection capacity of type-II Morris–Lecar neuron system under presynaptic bombardments

The information encoding mechanism of the neuronal system is quite complex and is sensitive to environmental conditions. Neuronal noise, especially synaptic random inputs, is a natural part of the brain. Theoretical and experimental studies have revealed that noise plays a vital role in signal frequency selectivity and weak sensory input perception of the neuronal system. There is a consensus that sufficiently intense noise can trigger rhythmic brain activity, and these noise-induced oscillations could improve signal processing of the neuronal system, particularly when the external signal frequency aligns with the frequency of the noise-induced rhythm. Such behavior in response to noise in the signal-processing mechanism of biological systems is elucidated by stochastic resonance. In this regard, this paper systematically analyzes the stochastic resonance in a Type-II Morris–Lecar neuron under excitatory and inhibitory background spike bombardments. Our results indicate that Morris–Lecar Type II neurons enhance their signal coding capacity by exploiting background synaptic activity. In addition, it has been revealed that the biological properties of the background synaptic connections of neurons that oscillate at different frequencies, such as delta, theta, alpha, beta, and gamma bands, are different. On the other hand, it has been found that neurons adapt to the properties of pre-synaptic neurons to encode weak signals. This study ensures novel insights into the functional role of background synaptic input in neuronal coding mechanisms by demonstrating a biophysical factor of stochastic resonance via numerical analyses. Furthermore, our results show that the properties of the background synaptic inputs significantly determine what kind of signal to encode or not. These results are an important indicator of the signal frequency selectivity of neurons, such as auditory cells.

Probabilistic Estimation and Control of Dynamical Systems Using Particle Filter with Adaptive Backward Sampling.

Estimating and controlling dynamical systems from observable time-series data are essential for understanding and manipulating nonlinear dynamics. This paper proposes a probabilistic framework for simultaneously estimating and controlling nonlinear dynamics under noisy observation conditions. Our proposed method utilizes the particle filter not only as a state estimator and a prior estimator for the dynamics but also as a controller. This approach allows us to handle the nonlinearity of the dynamics and uncertainty of the latent state. We apply two distinct dynamics to verify the effectiveness of our proposed framework: a chaotic system defined by the Lorenz equation and a nonlinear neuronal system defined by the Morris-Lecar neuron model. The results indicate that our proposed framework can simultaneously estimate and control complex nonlinear dynamical systems.

Biorealistic Neuronal Temperature-Sensitive Dynamics within Threshold Switching Memristors: Toward Neuromorphic Thermosensation.

Neuromorphic nanoelectronic devices that can emulate the temperature-sensitive dynamics of biological neurons are of great interest for bioinspired robotics and advanced applications such as in silico neuroscience. In this work, we demonstrate the biomimetic thermosensitive properties of two-terminal V3O5 memristive devices and showcase their similarity to the firing characteristics of thermosensitive biological neurons. The temperature-dependent electrical characteristics of V3O5-based memristors are used to understand the spiking response of a simple relaxation oscillator. The temperature-dependent dynamics of these oscillators are then compared with those of biological neurons through numerical simulations of a conductance-based neuron model, the Morris-Lecar neuron model. Finally, we demonstrate a robust neuromorphic thermosensation system inspired by biological thermoreceptors for bioinspired thermal perception and representation. These results not only demonstrate the biorealistic emulative potential of threshold-switching memristors but also establish V3O5 as a functional material for realizing solid-state neurons for neuromorphic computing and sensing applications.

Coupled Memristor Oscillators for Neuromorphic Locomotion Control: Modeling and Analysis.

The recent surge of interest in brain-inspired architectures along with the development of nonlinear dynamical electronic devices and circuits has enabled energy-efficient hardware realizations of several important neurobiological systems and features. Central pattern generator (CPG) is one such neural system underlying the control of various rhythmic motor behaviors in animals. A CPG can produce spontaneous coordinated rhythmic output signals without any feedback mechanism, ideally realizable by a system of coupled oscillators. Bio-inspired robotics aims to use this approach to control the limb movement for synchronized locomotion. Hence, devising a compact and energy-efficient hardware platform to implement neuromorphic CPGs would be of great benefit for bio-inspired robotics. In this work, we demonstrate that four capacitively coupled vanadium dioxide (VO2) memristor-based oscillators can produce spatiotemporal patterns corresponding to the primary quadruped gaits. The phase relationships underlying the gait patterns are governed by four tunable bias voltages (or four coupling strengths) making the network programmable, reducing the complex problem of gait selection and dynamic interleg coordination to the choice of four control parameters. To this end, we first introduce a dynamical model for the VO2 memristive nanodevice, then perform analytical and bifurcation analysis of a single oscillator, and finally demonstrate the dynamics of coupled oscillators through extensive numerical simulations. We also show that adopting the presented model for a VO2 memristor reveals a striking resemblance between VO2 memristor oscillators and conductance-based biological neuron models such as the Morris-Lecar (ML) model. This can inspire and guide further research on implementation of neuromorphic memristor circuits that emulate neurobiological phenomena.

Dynamics of a Piecewise-Linear Morris–Lecar Model: Bifurcations and Spike Adding

Dynamics of a Piecewise-Linear Morris–Lecar Model: Bifurcations and Spike Adding

Rapid changes in synchronizability in conductance-based neuronal networks with conductance-based coupling.

Real neurons connect to each other non-randomly. These connectivity graphs can potentially impact the ability of networks to synchronize, along with the dynamics of neurons and the dynamics of their connections. How the connectivity of networks of conductance-based neuron models like the classical Hodgkin-Huxley model or the Morris-Lecar model impacts synchronizability remains unknown. One powerful tool to resolve the synchronizability of these networks is the master stability function (MSF). Here, we apply and extend the MSF approach to networks of Morris-Lecar neurons with conductance-based coupling to determine under which parameters and for which graphs the synchronous solutions are stable. We consider connectivity graphs with a constant non-zero row sum, where the MSF approach can be readily extended to conductance-based synapses rather than the more well-studied diffusive connectivity case, which primarily applies to gap junction connectivity. In this formulation, the synchronous solution is a single, self-coupled, or "autaptic" neuron. We find that the primary determining parameter for the stability of the synchronous solution is, unsurprisingly, the reversal potential, as it largely dictates the excitatory/inhibitory potential of a synaptic connection. However, the change between "excitatory" and "inhibitory" synapses is rapid, with only a few millivolts separating stability and instability of the synchronous state for most graphs. We also find that for specific coupling strengths (as measured by the global synaptic conductance), islands of synchronizability in the MSF can emerge for inhibitory connectivity. We verified the stability of these islands by direct simulation of pairs of neurons coupled with eigenvalues in the matching spectrum.

Insights into oscillator network dynamics using a phase-isostable framework.

Networks of coupled nonlinear oscillators can display a wide range of emergent behaviors under the variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by the evolution of its phase and slowest decaying isostable coordinate have previously been shown to capture bifurcations and dynamics of the network, which cannot be explained through standard phase reduction. An alternative framework using isostable coordinates to obtain higher-order phase reductions has also demonstrated a similar descriptive ability for two oscillators. In this work, we consider the phase-isostable network equations for an arbitrary but finite number of identical coupled oscillators, obtaining conditions required for the stability of phase-locked states including synchrony. For the mean-field complex Ginzburg-Landau equation where the solutions of the full system are known, we compare the accuracy of the phase-isostable network equations and higher-order phase reductions in capturing bifurcations of phase-locked states. We find the former to be the more accurate and, therefore, employ this to investigate the dynamics of globally linearly coupled networks of Morris-Lecar neuron models (both two and many nodes). We observe qualitative correspondence between results from numerical simulations of the full system and the phase-isostable description demonstrating that in both small and large networks, the phase-isostable framework is able to capture dynamics that the first-order phase description cannot.

Effects of Josephson junction synapse on coupled Morris-Lecar neurons

Recently, various artificial synapses have been examined in neural networks for obtaining different dynamical characteristics of neurons. The Josephson junction can be used for constructing an artificial synapse that incorporates the external magnetic field effects. Using the Josephson junction for coupling the neurons involves the phase error between the junctions. This paper uses the Josephson junction and a linear resistor to connect two Morris-Lecar neuron models. The effects of Josephson junction parameters are investigated on the dynamical properties of neurons. The obtained bifurcation and Lyapunov exponent diagrams represent that the Josephson junction synapse significantly affects the neurons’ dynamics. Rich dynamics are observed by varying the junction parameters. Moreover, the multistability properties are reported. Finally, the synchronization of coupled neurons is studied under different junction's parameters.

Digital Hardware Implementation of Morris-Lecar, Izhikevich, and Hodgkin-Huxley Neuron Models With High Accuracy and Low Resources

Digital Hardware Implementation of Morris-Lecar, Izhikevich, and Hodgkin-Huxley Neuron Models With High Accuracy and Low Resources

Signal encoding performance of astrocyte-dressed Morris Lecar neurons

There are more support cells called glia in the central nervous system than neurons. Although previous studies have shown that one of these glial cells, astrocytes, can communicate with neurons bidirectionally, giving a silent neuron the ability to fire or changing the neuron’s firing frequency, understanding the role of astrocytes in neuroscience is still in its infancy. With this motivation, in this study, the weak signal encoding performance of different types of astrocyte-dressed Morris Lecar neurons in the presence of noise naturally found in biological systems is systematically investigated. The results showed that astrocyte-dressed Morris Lecar neurons had a subthreshold signal frequency suitable for optimal encoding and that Morris Lecar neurons resonated at this frequency. In addition, the rate of inositol trisphosphate production in the astrocyte has been shown to affect signal detection at different noise intensities and coupling strengths. Finally, simulations performed by including the internal noise of the astrocytes originating from calcium ion channels in the model have shown how the signal transmission changes depending on the calcium channel number, noise intensity, and coupling strength. In this context, the presented study also contains important information in terms of examining stochastic astrocyte dynamics that affect the weak signal detection performance of different types of astrocyte-dressed Morris Lecar neurons.

An advanced approach for the electrical responses of discrete fractional-order biophysical neural network models and their dynamical responses

The multiple activities of neurons frequently generate several spiking-bursting variations observed within the neurological mechanism. We show that a discrete fractional-order activated nerve cell framework incorporating a Caputo-type fractional difference operator can be used to investigate the impacts of complex interactions on the surge-empowering capabilities noticed within our findings. The relevance of this expansion is based on the model’s structure as well as the commensurate and incommensurate fractional-orders, which take kernel and inherited characteristics into account. We begin by providing data regarding the fluctuations in electronic operations using the fractional exponent. We investigate two-dimensional Morris–Lecar neuronal cell frameworks via spiked and saturated attributes, as well as mixed-mode oscillations and mixed-mode bursting oscillations of a decoupled fractional-order neuronal cell. The investigation proceeds by using a three-dimensional slow-fast Morris–Lecar simulation within the fractional context. The proposed method determines a method for describing multiple parallels within fractional and integer-order behaviour. We examine distinctive attribute environments where inactive status develops in detached neural networks using stability and bifurcation assessment. We demonstrate features that are in accordance with the analysis’s findings. The Erdös–Rényi connection of asynchronization transformed neural networks (periodic and actionable) is subsequently assembled and paired via membranes that are under pressure. It is capable of generating multifaceted launching processes in which dormant neural networks begin to come under scrutiny. Additionally, we demonstrated that boosting connections can cause classification synchronization, allowing network devices to activate in conjunction in the future. We construct a reduced-order simulation constructed around clustering synchronisation that may represent the operations that comprise the whole system. Our findings indicate the influence of fractional-order is dependent on connections between neurons and the system’s stored evidence. Moreover, the processes capture the consequences of fractional derivatives on surge regularity modification and enhance delays that happen across numerous time frames in neural processing.

An energy-efficient hybrid CMOS spiking neuron circuit design with a memristive based novel T-type artificial synapse

Applications exploiting Artificial Intelligence (AI) have grown rapidly and are encountered in significant energy consumption. The organic neurons used in digital computers are mimicked by artificial neural networks (based on AI). In this perspective, AI’s Conventional computing technology, relying on the Von Neumann structure, is approaching the end of Moore’s law. To solve this problem, the memristor device concept is identified as a futuristic option for the design of neurons and synapses. The primary component of the central nervous system is the neuron, that serves as one of the crucial building blocks in the hardware implementation of spiking neural networks. Energy efficiency, power, and firing frequency are major constraints in the modelling of neurons. This work delivers the development of neurons using a Hybrid CMOS Memristor (HCM) Morris–Lecar (ML) model with a novel T-type synapse. Low power consumption in nano-watts, reduction in circuit complexity, and energy efficiency in femtojoules are the key benefits achieved through the proposed neuron model. Here, the achieved power consumption, energy efficiency, and spike frequency are 17.42 pW, 1.05 fJ, and 28.52 kHz, respectively. In addition, Moreover the achieved spike frequency in the order of kHz is helpful to advance biological plausibility.

Noise-Induced Toroidal Bursting Oscillations and Coherence Resonance in the Morris–Lecar–Terman Model

We study the three-dimensional Morris–Lecar–Terman neuron model in the parametric region of tonic spiking oscillations close to the bifurcation of the torus birth. It is shown that in this region random disturbances can induce switching to the toroidal bursting mode from the tonic spiking regime. We approximate the probability of such switches as well as analyze temporal characteristics of produced oscillations. Moreover, we indicate a coherence resonance in the stochastic bursting regime and reveal the underlying reasons of these noise-induced phenomena.

Coexisting firing patterns and circuit design of locally active memristive autapse morris-lecar neuron

A novel bistable locally active memristor is proposed in this paper. A locally active memristive autapse Morris-Lecar neuron model is constructed by using memristor to simulate the autapse of neuron. The equilibrium point and stability of the system are analyzed, and the firing mode and bifurcation characteristics of the neuronal system are revealed by using dynamic analysis methods such as slow-fast dynamics, interspike interval bifurcation diagrams, Lyapunov exponents, phase diagrams and time series diagram. By changing the memristive autapse gain and the initial state of the system, the existence of coexisting firing patterns in the constructed neuron model is confirmed. Finally, to further verify the effectiveness of the numerical simulation, the analog equivalent circuit of the locally active memristive neuron system is designed, which proves that the system is physically realizable.

A study on weak signal detection of dressed Morris Lecar neuron in chaotic environment

A study on weak signal detection of dressed Morris Lecar neuron in chaotic environment

Stochastic Morris–Lecar model with time delay under magnetic field excitation

In this paper, a four-dimensional Morris–Lecar (M–L) model with a memristor is improved by introducing synaptic dynamics, and an M–L model with time delay and Gaussian white noise is established. The stability of the model at the equilibrium point was demonstrated theoretically, and the correctness of the theory was verified by numerical simulations. In the numerical simulation, the model is found to have multiple discharge modes of spike discharge, cluster discharge, chaotic discharge, and coexistence of multiple discharge modes by changing important parameters such as time delay, magnetic field feedback strength, and noise intensity. This lays the foundation for further exploration of the M–L neuron coupling model with time delay and noise as well as the study of synchronization of neuronal networks.

Analog Spiking Neural Network Synthesis for the MNIST

Different from classical artificial neural network which processes digital data, the spiking neural network (SNN) processes spike trains. Indeed, its event-driven property helps to capture the rich dynamics the neurons have within the brain, and the sparsity of collected spikes helps reducing computational power. Novel synthesis framework is proposed and an algorithm is detailed to guide designers into deep learning and energy-efficient analog SNN using MNIST. An analog SNN composed of 86 electronic neurons (eNeuron) and 1238 synapses interacting through two hidden layers is illustrated. Three different models of eNeurons implementations are tested, being (Leaky) Integrate-and-Fire (LIF), Morris Lecar (ML) simplified (simp.) and biomimetic (bio.). The proposed SNN, coupling deep learning and ultra-low power, is trained using a common machine learning system (Tensor- Flow) for the MNIST. LIF eNeurons implementations present some limitations and weakness in terms of dynamic range. Both ML eNeurons achieve robust accuracy which is approximately of 0.82.