Morris-Lecar Neuron 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.

Mixed-mode oscillations in a three-timescale coupled Morris-Lecar system.

Mixed-mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale systems can arise either from a canard mechanism associated with folded node singularities or a delayed Andronov-Hopf bifurcation (DHB) of the fast subsystem. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in coupled Morris-Lecar neurons with three distinct timescales. We investigate two kinds of MMOs occurring in the presence of a singularity known as canard-delayed-Hopf (CDH) and in cases where CDH is absent. In both cases, we examine how features and mechanisms of MMOs vary with respect to variations in timescales. Our analysis reveals that MMOs supported by CDH demonstrate significantly stronger robustness than those in its absence. Moreover, we show that the mere presence of CDH does not guarantee the occurrence of MMOs. This work yields important insights into conditions under which the two separate mechanisms in two-timescale context, canard and DHB, can interact in a three-timescale setting and produce more robust MMOs, particularly against timescale variations.

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.

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

Diverse electrical responses in a network of fractional-order conductance-based excitable Morris-Lecar systems

The diverse excitabilities of cells often produce various spiking-bursting oscillations that are found in the neural system. We establish the ability of a fractional-order excitable neuron model with Caputo’s fractional derivative to analyze the effects of its dynamics on the spike train features observed in our results. The significance of this generalization relies on a theoretical framework of the model in which memory and hereditary properties are considered. Employing the fractional exponent, we first provide information about the variations in electrical activities. We deal with the 2D class I and class II excitable Morris-Lecar (M-L) neuron models that show the alternation of spiking and bursting features including MMOs & MMBOs of an uncoupled fractional-order neuron. We then extend the study with the 3D slow-fast M-L model in the fractional domain. The considered approach establishes a way to describe various characteristics similarities between fractional-order and classical integer-order dynamics. Using the stability and bifurcation analysis, we discuss different parameter spaces where the quiescent state emerges in uncoupled neurons. We show the characteristics consistent with the analytical results. Next, the Erdös-Rényi network of desynchronized mixed neurons (oscillatory and excitable) is constructed that is coupled through membrane voltage. It can generate complex firing activities where quiescent neurons start to fire. Furthermore, we have shown that increasing coupling can create cluster synchronization, and eventually it can enable the network to fire in unison. Based on cluster synchronization, we develop a reduced-order model which can capture the activities of the entire network. Our results reveal that the effect of fractional-order depends on the synaptic connectivity and the memory trace of the system. Additionally, the dynamics captures spike frequency adaptation and spike latency that occur over multiple timescales as the effects of fractional derivative, which has been observed in neural computation.

Energy balance via memristor synapse in Morris-Lecar two-neuron network with FPGA implementation

Synapses can regulate the energy balance in the neural network. In this work, a two-neuron network is established by coupling two Morris-Lecar neurons using a memristor synapse. The periodic/hyperchaotic spiking-bursting patterns in the two-neuron network are portrayed using bifurcation plot, phase portrait, and time-domain waveform. The asynchronous behaviors exhibited by the numerical results show the difference of the inner field energy of individual neurons. To investigate the biophysical mechanism in the two-neuron network, the Hamiltonian energy function of a single neuron is derived by Helmholtz's theorem to equivalently describe its inner field energy, and the bioelectric activities are analyzed in combination with synchronization error functions. It is revealed that the initial state of memristor synapse can regulate the energy diversity in the two-neuron network and achieve the energy balance in the transient state. Two neurons firing in hyperchaotic pattern exchange field energy through the memristor synapse as a coupling channel until energy balance and complete synchronization. In the complete synchronization state, the memristor synapse is silent, which leads to the retrograding of hyperchaotic firing behaviors. Finally, an FPGA-based digital electronic two-neuron network is developed, and the experimental measurements well confirm the numerical simulations of bioelectric activities.

Investigation of chaotic resonance in Type-I and Type-II Morris-Lecar neurons

The signal encoding capacity of the nervous system is significantly related to the spiking regime of neurons, and the firing behaviors of neurons are vibrant due to their complex structure. Chaotic fluctuations emerge at both micro and macro levels in the neuronal medium. It is thought that chaotic oscillations are the beneficial component, rather than disruptive, for cognitive functions of the nervous system. It is found that external chaotic activity at a suitable level enhances the weak signal encoding performance of neurons, particularly when the weak signal frequency is chosen close to that of the chaotic fluctuations-induced sub-threshold oscillations frequencies. This manipulation of the signal encoding performance of neurons by chaotic fluctuations is explained by the “chaotic resonance” phenomenon. In the current work, we systematically examine the impacts of the extrinsic chaotic stimulus from the Lorenz system on the subthreshold periodic signal encoding performance of Type-I and Type-II Morris-Lecar neurons. Our results show that weak signal encoding performance of both Type-I and Type-II Morris-Lecar neurons exhibits resonance behavior and its resonance mainly depends on external chaotic current intensity. Also, we reveal that suitable chaotic current level for the best encoding in Morris-Lecar neurons of the sub-threshold signal changes with signal frequency. In addition, we indicate that there is a frequency range in which Morris-Lecar neurons are sensitive to signals. We also demonstrate the existence of a chaotic current intensity range at these frequencies, enabling neurons to improve weak signal encoding performance. Finally, it is observed that the frequency ranges in which Type-I and Type-II neurons are sensitive to weak signals are quite different. In this regard, our research provides important insights into the possible roles of chaotic resonance in the weak signal encoding of different types of neurons.

Design and Analysis of the Morris–Lecar Spiking Neuron in Efficient Analog Implementation

We propose the design and analysis of the Morris-Lecar spiking neuron in optimized analog implementation from a methodical standpoint to frame the neuron design within a theoretical context targeting the design of efficient solutions for the low-complexity analog implementation of Spiking Neural Networks (SNNs). In the proposed neuron CMOS circuit, the most chip area-consumer elements that are generally a leakage resistor and state capacitors have been crossed off while the neuron excitation stimuli is adjusted through an on-chip single transistor. Furthermore, the proposed analysis is potentially investigated to enhance the reliability and robustness of the analog system by embracing the effects of intrinsic random manufacturing process variations. The study is developed based on a 45nm standard CMOS technology for low power applications.

Firing patterns and synchronization of Morris-Lecar neuron model with memristive autapse

Autapse is a self-feedback current in some neurons that can substantially affect the neuron’s characteristics. Due to the importance of electromagnetic induction in the dynamical functions of the neurons, the memristive autapses have been introduced. This paper presents the 3D Morris-Lecar neuron model with a memristive autapse. The dynamics of the memristive autaptic model are investigated by varying autapse parameters. It is revealed that the memristive autapse can change the period of the neuron’s firing or even change its dynamics between periodic and chaotic firings. The results represent that the chaotic regions are extended with the increase in the autapse time delay. Moreover, the memristive autapse leads to the emergence of multistability. The synchronization of coupled memristive autaptic neurons is also examined. It is found that the synchronization of chaotic neurons is enhanced by considering the memristive autapse. With increasing the autapse gain, the required coupling strength for synchronization decreases.

Multistability and evolution of chimera states in a network of type II Morris-Lecar neurons with asymmetrical nonlocal inhibitory connections.

Formation of synchronous activity patterns is an essential property of neuronal networks that has been of central interest to synchronization theory. Chimera states, where both synchronous and asynchronous activities of neurons co-exist in a single network, are particularly poignant examples of such patterns, whose dynamics and multistability may underlie brain function, such as cognitive tasks. However, dynamical mechanisms of coherent state formation in spiking neuronal networks as well as ways to control these states remain unclear. In this paper, we take a step in this direction by considering the evolution of chimera states in a network of class II excitable Morris-Lecar neurons with asymmetrical nonlocal inhibitory connections. Using the adaptive coherence measure, we are able to partition the network parameter space into regions of various collective behaviors (antiphase synchronous clusters, traveling waves, different types of chimera states as well as a spiking death regime) and have shown multistability between the various regimes. We track the evolution of the chimera states as a function of changed key network parameters and found transitions between various types of chimera states. We further find that the network can demonstrate long transients leading to quasi-persistence of activity patterns in the border regions hinting at near-criticality behaviors.