Neuronal Coupling Research Articles

The dynamical behavior effects of different numbers of discrete memristive synaptic coupled neurons

The dynamical behavior effects of different numbers of discrete memristive synaptic coupled neurons

Cross-Channel Color Image Encryption Scheme Based on Discrete Memristive Coupled Neurons and DWT Compression

To address the consumption and security of color images for transmission and storage, a cross-channel color image encryption scheme based on a discrete memristive coupled neuron model and DWT compression is designed in this article. Firstly, the dynamics of the discrete memristive coupled neuron system are analyzed and found to possess the hyperchaotic phenomenon, which provides sufficient security for the encryption scheme. Secondly, the color image processed by discrete wavelet transform (DWT) has a quarter of the previous capacity. Then, the color image is combined with a Hash function, and the resulting Hash sequence is given the initial value of the hyperchaotic system. Next, a particle swarm foraging algorithm (PSFA) is designed to better disrupt the correlation in the RGB channel. Finally, a complementary DNA coding rule is implemented for the further encryption of color images. Simulation results show that even with DWT lossy compression, the recovered image can be clearly seen. The performance analysis illustrates that under the hyperchaotic system, the proposed encryption algorithm brings higher security for color images.

Investigation of Synchronization Control of the Memristive/Resistive-Coupled Neural Network with Noise Effect

This study comprehensively investigates synchronization control of the memristive- and resistive-coupled neural network with noise effect. In this context, a sub-network is constructed with three chaotic memristive Hindmarsh–Rose neurons coupled by the memristive synapses. Then, two equivalent sub-networks are linked by the diffusive resistive synapse under a distinctive global network structure including two sub-networks. Thus, a double (memristive/resistive) control mechanism is used to achieve the synchronization state. The first mechanism is the memristive synaptic coupling in each sub-network, and the second one is the diffusive resistive coupling between two sub-networks constructing the global network. The synchronization between the neurons is proven theoretically through the Lyapunov stability and Lipschitz theorems and this proof process is verified with numerical experiments. According to the theoretical and numerical results, by adjusting memristive/resistive synaptic coupling weights, a synchrony behavior is generated successfully in these sub-networks and global networks. Additionally, this paper also handles the Gaussian white noise effect on the global network to examine continuity capability and stability of synchronization. Two different frameworks are built by applying the noise with multiple noise power levels and periods to (i) one of the resistive coupling neurons in each sub-network directly and (ii) one neuron in a sub-network without direct contact with the other sub-network. With these two characteristic designs, it is proven that the second design provides more robust characteristics since it utilizes the double control mechanism, which enhances the stability throughout external interferences enabling the network to sustain synchronous states.

Dynamics of Leaky Integrate‐and‐Fire Neurons Based on Oxyvanite Memristors for Spiking Neural Networks

Neuromorphic computing implemented with spiking neural networks (SNNs) based on volatile threshold switching is an energy‐efficient computing paradigm that may overcome future limitations of the von Neumann architecture. Herein, threshold switching in oxyvanite (V3O5) memristors and their application as a leaky integrate‐and‐fire (LIF) neuron are explored. The spiking response of individual neurons is examined as a function of circuit parameters, input pulse train, and temperature and reveals a pulse height‐dependent spike rate in which devices exhibit excitatory spiking behavior under low input voltages and protective inhibition spiking under high voltages. Resistively coupled LIF neurons are shown to exhibit additional neural functionalities (i.e., phasic, regular and adaptation, etc.) depending on the input voltage and circuit parameters. The behavior of both individual and coupled neurons is shown to be described by a physics‐based lumped element circuit model, which therefore provides a solid foundation for exploring more complex systems. Finally, the performance of a perceptron SNN employing these LIF neurons is assessed by simulating the classification of image recognition algorithm. These results advance the development of robust solid‐state neurons with low power consumption for neuromorphic computing.

Impact of white noise in artificial neural networks trained for classification: Performance and noise mitigation strategies.

In recent years, the hardware implementation of neural networks, leveraging physical coupling and analog neurons has substantially increased in relevance. Such nonlinear and complex physical networks provide significant advantages in speed and energy efficiency, but are potentially susceptible to internal noise when compared to digital emulations of such networks. In this work, we consider how additive and multiplicative Gaussian white noise on the neuronal level can affect the accuracy of the network when applied for specific tasks and including a softmax function in the readout layer. We adapt several noise reduction techniques to the essential setting of classification tasks, which represent a large fraction of neural network computing. We find that these adjusted concepts are highly effective in mitigating the detrimental impact of noise.

Coexisting firing patterns and attractor selection in memristive synapse coupled heterogeneous neurons

In this paper, we present a novel heterogeneous neuron network involving the coupling of a two-dimensional (2D) continuous Rulkov model with a 2D Hindmarsh-Rose (HR) neuron via memristive synapse. The present memristive coupled neuron network can produce an infinite number of coexisting hidden attractors with the same shape but located at different positions in the phase space, resulting in the interesting phenomenon of hidden homogeneous extreme multistability. Firstly, we study complex dynamical behaviors in detail through bifurcation diagrams, Lyapunov exponents, time series and phase portraits. Secondly, to select the desired firing pattern, a control method based on the feedback term is applied to the model. It is observed that the addition of this space-dependent feedback term to the dynamic equation of this model effectively eliminates all undesired firing patterns among the coexisting ones, and drives the heterogeneous neuron network to transition from coexisting hidden firing patterns to the expected firing pattern. Finally, Multisim circuit simulation is performed and the results are in line with numerical simulation.

Hamiltonian energy in a modified Hindmarsh-Rose model.

This paper investigates the Hamiltonian energy of a modified Hindmarsh-Rose (HR) model to observe its effect on short-term memory. A Hamiltonian energy function and its variable function are given in the reduced system with a single node according to Helmholtz's theorem. We consider the role of the coupling strength and the links between neurons in the pattern formation to show that the coupling and cooperative neurons are necessary for generating the fire or a clear short-term memory when all the neurons are in sync. Then, we consider the effect of the degree and external stimulus from other neurons on the emergence and disappearance of short-term memory, which illustrates that generating short-term memory requires much energy, and the coupling strength could further reduce energy consumption. Finally, the dynamical mechanisms of the generation of short-term memory are concluded.

Qualitative switches in single-neuron spike dynamics on neuromorphic hardware: implementation, impact on network synchronization and relevance for plasticity

Abstract Most efforts on spike-based learning on neuromorphic hardware focus on synaptic plasticity and do not yet exploit the potential of altering the spike-generating dynamics themselves. Biological neurons show distinct mechanisms of spike generation, which affect single-neuron and network computations. Such a variety of spiking mechanisms can only be mimicked on chips with more advanced, nonlinear single-neuron dynamics than the commonly implemented leaky integrate-and-fire (LIF) neurons. Here, we demonstrate that neurons on the BrainScaleS-2 chip configured for exponential leaky integrate-and-fire (EIF) dynamics can be tuned to undergo a qualitative switch in spike generation via a modulation of the reset voltage. This switch is accompanied by altered synchronization properties of neurons in a network and thereby captures a main characteristic of the unfolding of the saddle-node loop (SNL) bifurcation - a qualitative transition that was recently demonstrated in biological neurons. Using this switch, cell-intrinsic properties alone provide a means to control whether small networks of all-to-all coupled neurons on the chip exhibit synchronized firing or splayed-out spiking patterns. We use an example from a central pattern generating circuit in the fruitfly to show that such dynamics can be induced and controlled on the chip. Our study thereby demonstrates the potential of neuromorphic chips with relatively complex and tunable single-neuron dynamics such as the BrainScaleS-2 chip, to generate computationally distinct single unit dynamics. We conclude with a discussion of the utility of versatile spike-generating mechanisms on neuromorphic chips.

Synchronization of delayed coupled neurons with multiple synaptic connections.

Synchronization is a key feature of the brain dynamics and is necessary for information transmission across brain regions and in higher brain functions like cognition, learning and memory. Experimental findings demonstrated that in cortical microcircuits there are multiple synapses between pairs of connected neurons. Synchronization of neurons in the presence of multiple synaptic connections may be relevant for optimal learning and memory, however, its effect on the dynamics of the neurons is not adequately studied. Here, we address the question that how changes in the strength of the synaptic connections and transmission delays between neurons impact synchronization in a two-neuron system with multiple synapses. To this end, we analytically and computationally investigated synchronization dynamics by considering both phase oscillator model and conductance-based Hodgkin-Huxley (HH) model. Our results show that symmetry/asymmetry of feedforward and feedback connections crucially determines stability of the phase locking of the system based on the strength of connections and delays. In both models, the two-neuron system with multiple synapses achieves in-phase synchrony in the presence of small and large delays, whereas an anti-phase synchronization state is favored for median delays. Our findings can expand the understanding of the functional role of multisynaptic contacts in neuronal synchronization and may shed light on the dynamical consequences of pathological multisynaptic connectivity in a number of brain disorders.

Reproduced neuron-like excitability and bursting synchronization of memristive Josephson junctions loaded inductor

Employing electronic component including memristor and Josephson junction to mimic biological neuron or synapse has elicited intense research in recent years. Neurons described by nonlinear oscillators can exhibit complex electrical activities. Josephson junctions are excellent candidates for neuron-inspired components because of their physical properties with low energy costs and high efficiency. In this paper, we revisit a prior work on memristive Josephson junction (MJJ) to identify the dynamical mechanisms to mimic neuron-like excitability and spiking. The inductive memristive Josephson junction (L-MJJ) model is further developed by adding an inductor with internal resistor. It is found that the L-MJJ model can reproduce square-wave bursting of the classical neuronal model from the neurodynamics point of view. The coupling L-MJJ oscillators can achieve in-phase and antiphase bursting synchronization similar with nonlinear coupling neurons. From the framework of nonlinear dynamics theory, this work aspires to build effective bridge between superconducting physics and theoretical neuroscience. Obtained results confirm the potential feasibility of this junction in designing a neuron-inspired computation to explore dynamics of larger-scale neuromorphic network.

Dynamics of Hindmarsh–Rose neurons connected via adaptive memristive synapse

Experimental data suggest that temporal neural activity regulates the synaptic weight, a phenomenon known as activity-dependent synaptic plasticity. Thus far, a diversity of neuronal learning rules have been adopted; a likely one is a Hebbian adaptation based on neuron synchrony. Regarding the growing appeal for coupling neurons through memristors, an element bridging magnetic flux and ion exchange, the existing literature on adapting memristive synapses seems limited. This paper aims to investigate two Hindmarsh–Rose neurons coupled through an adaptive memristor synapse by treating adaptive coupling parameters as bifurcation parameters. The capability of adaptive memristive coupling to generate high periodic and chaotic oscillations in the intrinsic periodic behavior of HR neurons is revealed. Synchronization analysis suggests that bifurcation scenarios are closely associated with the transition of the generic firings of two neurons from asynchrony to perfect synchrony. The Hamilton energy analysis indicates that as two neurons transition to synchrony, their energy levels equalize, and the energy fluctuations within the memristive coupling channel diminish. The value of the adaption parameter by which neurons synchronize also depends on the intrinsic parameters of HR, particularly the one associated with the effectiveness of slow channels. Additionally, the synchronization's robustness against different noise intensities has been examined. At last, on the matter of multistability, several pieces of evidence also exist.

Desynchronization of neuronal firing in multiparameter ultrasound stimulation

Low-intensity transcranial ultrasound stimulation, a novel neuromodulation technique, that possesses the advantages of non-invasiveness, high penetration depth, and high spatial resolution, has achieved positive neuromodulation effects in animal studies. But the regulatory mechanism remains controversial. The intramembrane cavitation effect is considered one of the mechanisms for ultrasound neuromodulation. In this study, the modified equations of ultrasonic cavitation bubble dynamics were coupled with the dual-coupled neuron Hindmarsh-Rose model, small-world neural network model, and the Jansen-Rit neural mass model, which simulate simple coupled neurons, complex neuronal networks, and discharge signals in epileptic disorders respectively. The results demonstrated that ultrasound stimulation has an appreciable modulatory effect on neuronal firing desynchronization in Hindmarsh-Rose model and small-world neural network model. The desynchronization effect is related to the stimulation frequency and intensity. Furthermore, ultrasound stimulation has an inhibitory effect on epileptic seizures, and the effect is enhanced by increasing ultrasound frequency from 0.1–1.0 MHz. This is the first combination of ultrasonic intramembrane cavitation effect theory with neurons and neural network firing desynchronization, which can provide guidance of parametric and theories support for the studies of neurological diseases such as epilepsy and Parkinson’s disease.

Passive Membrane Properties and Spike Characteristics in a Pair of Identified Electrically Coupled Lymnaea stagnalis Neurons under Long-Term Experimental Hyperglycemia

Passive Membrane Properties and Spike Characteristics in a Pair of Identified Electrically Coupled Lymnaea stagnalis Neurons under Long-Term Experimental Hyperglycemia

Complex Dynamics of Coupled Neurons Through a Memristive Synapse: Extreme Multistability and Its Control With Selection of the Desired State

In this contribution, a new configuration involving the coupling of a 2D Fitzhugh-Nagumo (FN) neuron with a 3D Hindmarsh-Rose (HR) neuron via a memristive synapse is investigated. The self-excited dynamics of the coupled neurons is revealed after the analysis of the equilibria of the model. During the numerical investigation of the model, resting activity, periodic spikes, periodic and chaotic bursts are found. More interestingly, the coupled neurons display the striking and rare phenomenon of homogeneous extreme multistability. It corresponds to the coexistence of an infinite number of firing activities of the same nature but located at different levels in the phase space. Furthermore, the selection of the desired electrical activity dynamics is also underlined through the noninvasive control scheme. Finally, an electronic circuit of the coupled neuron is designed and investigated in the Pspice environment to further support the obtained results.

Firing mechanism based on single memristive neuron and double memristive coupled neurons

Memristive neurons and memristive neural networks constructed based on memristors have important research significance for revealing the mystery of the brain. This paper proposes a compound hyperbolic tangent cubic nonlinear memristor, which has nonvolatile memory characteristics and local activity characteristics. In particular, the memristor also has three stable pinched hysteresis loops under different initial values. The memristor is applied to Fitzhugh–Nagumo neuron and Hindmarsh–Rose neuron to establish five different memristive neural models, and a series of firing dynamics analysis are carried out on them. At the same time, we not only discuss multiple firing patterns on a single memristive neuron and double memristive coupled neurons, but also compare which neuron and which coupled neural network the proposed memristor is more suitable for, which is a lack of comprehensive investigation in the published research. Furthermore, digital circuit experiment is performed on the FPGA development board to verify the firing mechanism of these memristive neural models, which has potential application value for some practical projects.

Lotus: a memory organization for loose and tight coupling neurons in neuromorphic architecture

Lotus: a memory organization for loose and tight coupling neurons in neuromorphic architecture

Timing-Dependent Potentiation and Depression of Electrical Synapses Contribute to Network Stability in the Crustacean Cardiac Ganglion.

Central pattern generators produce many rhythms necessary for survival (e.g., chewing, breathing, locomotion), and doing so often requires coordination of neurons through electrical synapses. Because even neurons of the same type within a network are often differentially tuned, uniformly applied neuromodulators or toxins can result in uncoordinated activity. In the crab (Cancer borealis) cardiac ganglion, potassium channel blockers and serotonin cause increased depolarization of the five electrically coupled motor neurons as well as loss of the normally completely synchronous activity. Given time, compensation occurs that restores excitability and synchrony. One of the underlying mechanisms of this compensation is an increase in coupling among neurons. However, the salient physiological signal that initiates increased coupling has not been determined. Using male C. borealis, we show that it is the loss of synchronous voltage signals between coupled neurons that is at least partly responsible for plasticity in coupling. Shorter offsets in naturalistic activity across a gap junction enhance coupling, whereas longer delays depress coupling. We also provide evidence on why a desynchronization-specific potentiation or depression of the synapse could ultimately be adaptive through using a hybrid network created by artificially coupling two cardiac ganglia. Specifically, a stray neuron may be brought back in line by increasing coupling if its activity is closer to the remainder of the network. However, if a the activity of a neuron is far outside network parameters, it is detrimental to increase coupling, and therefore depression of the synapse removes a potentially harmful influence on the network.SIGNIFICANCE STATEMENT Understanding how neural networks maintain output over years despite environmental and physiological challenges requires understanding the regulatory principles of these networks. Here, we study how cells that are synchronously active at baseline respond to becoming desynchronized. In this system, a loss of synchrony causes different parts of the heart to receive uncoordinated stimulation. We find a calcium-dependent control mechanism that alters the strength of electrical connections between motor neurons. Although others have described similar control mechanisms, here, we demonstrate that voltage changes are sufficient to elicit regulation. Furthermore, we demonstrate that strong connections in a sufficiently perturbed network can prevent any neuron from producing its target activity, thus suggesting why the connections are not constitutively as strong as possible.

Bifurcations and Chaos in Periodically Forced Coupled Ramp Neurons

Bifurcations and chaos in periodically forced coupled ramp neurons (rectified linear units) are examined as one of minimal chaotic neural networks. The first ramp neuron connects to the second ramp neuron excitatorily while the second ramp neuron connects to the first neuron inhibitorily. When the first ramp neuron is forced by a rectangular wave, a stable periodic solution is generated. The system is piecewise linear and its periodic solutions are obtained by connecting local solutions in linear domains at borders and solving transcendental equations. Their Poincaré maps and Jacobian matrices are also derived rigorously, by which the bifurcations of the periodic solutions are calculated. The periodic solution undergoes period-doubling bifurcations, which leads to the generation of a chaotic attractor. A period-three solution is also generated through saddle-node bifurcations, which is characteristic of a chaotic system. A one-dimensional phase return map is derived and it is shown that the bifurcations of its fixed points agree with the bifurcations of the multiple periodic solutions of the original forced system. Further, qualitatively the same bifurcations and chaos occur when the first ramp neuron is replaced by a step neuron, in which a chaotic attractor is also generated through a border collision bifurcation. The linear response and the dead zone of the ramp neurons are essential for the emergence of chaos.

On the Diverse Functions of Electrical Synapses.

Electrical synapses are the neurophysiological product of gap junctional pores between neurons that allow bidirectional flow of current between neurons. They are expressed throughout the mammalian nervous system, including cortex, hippocampus, thalamus, retina, cerebellum, and inferior olive. Classically, the function of electrical synapses has been associated with synchrony, logically following that continuous conductance provided by gap junctions facilitates the reduction of voltage differences between coupled neurons. Indeed, electrical synapses promote synchrony at many anatomical and frequency ranges across the brain. However, a growing body of literature shows there is greater complexity to the computational function of electrical synapses. The paired membranes that embed electrical synapses act as low-pass filters, and as such, electrical synapses can preferentially transfer spike after hyperpolarizations, effectively providing spike-dependent inhibition. Other functions include driving asynchronous firing, improving signal to noise ratio, aiding in discrimination of dissimilar inputs, or dampening signals by shunting current. The diverse ways by which electrical synapses contribute to neuronal integration merits furthers study. Here we review how functions of electrical synapses vary across circuits and brain regions and depend critically on the context of the neurons and brain circuits involved. Computational modeling of electrical synapses embedded in multi-cellular models and experiments utilizing optical control and measurement of cellular activity will be essential in determining the specific roles performed by electrical synapses in varying contexts.

A Scalar Poincaré Map for Anti-phase Bursting in Coupled Inhibitory Neurons With Synaptic Depression.

Short-term synaptic plasticity is found in many areas of the central nervous system. In the inhibitory half-center central pattern generators involved in locomotion, synaptic depression is believed to act as a burst termination mechanism, allowing networks to generate anti-phase bursting patterns of varying periods. To better understand burst generation in these central pattern generators, we study a minimal network of two neurons coupled through depressing synapses. Depending on the strength of the synaptic conductance between the two neurons, this network can produce symmetric n : n anti-phase bursts, where neurons fire n spikes in alternation, with the period of such solutions increasing with the strength of the synaptic conductance. Relying on the timescale disparity in the model, we reduce the eight-dimensional network equations to a fully-explicit scalar Poincaré burst map. This map tracks the state of synaptic depression from one burst to the next and captures the complex bursting dynamics of the network. Fixed points of this map are associated with stable burst solutions of the full network model, and are created through fold bifurcations of maps. We derive conditions that predict the bifurcations between n : n and (n + 1) : (n + 1) solutions, producing a full bifurcation diagram of the burst cycle period. Predictions of the Poincaré map fit excellently with numerical simulations of the full network model and allow the study of parameter sensitivity for rhythm generation.