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.

Dynamics of firing patterns,synchronization and resonances in neuronal electrical activities:experiments and analysis

Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast-slow dynamics analysis for classification and mechanism of various bursting patterns, one- or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities （stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.）. Thirdly, different types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.

In- and Anti-transition of Firing Patterns Induced by Random Long-range Connections in Coupled Hindmarsh-Rose Neurons System

The effects of random long-range connections （shortcuts） on the transitions of neural firing patterns in coupled Hindmarsh-Rose neurons are investigated, where each neuron is subjected to an external current. It is found that, on one hand, the system can achieve the transition of neural firing patterns from the fewer-period state to the multi-period one, when the number of the added shortcuts in the neural network is greater than a threshold value, indicating the occurrence of in-transition of neural firing patterns. On the other hand, for a stronger coupling strength, we can also find the similar but reverse results by adding some proper random connections. In addition, the influences of system size and coupling strength on such transition behavior, as well as the internality between the transition degree of firing patterns and its critical characteristics for different external stimulation current, are also discussed.

Dynamics analysis on neural firing patterns by symbolic approach

Neural firing patterns are investigated by using symbolic dynamics. Bifurcation behaviour of the Hindmarsh-Rose （HR） neuronal model is simulated with the external stimuli gradually decreasing, and various firing activities with different topological structures are orderly numbered. Through constructing first-return maps of interspike intervals, all firing patterns are described and identified by symbolic expressions. On the basis of ordering rules of symbolic sequences, the corresponding relation between parameters and firing patterns is established, which will be helpful for encoding neural information. Moreover, using the operation rule of ＊ product, generation mechanisms and intrinsic configurations of periodic patterns can be distinguished in detail. Results show that the symbolic approach is a powerful tool to study neural firing activities. In particular, such a coarse-grained way can be generalized in neural electropt/ysiological experiments to extract much valuable information from complicated experimental data.

Responses from two firing patterns in inferior colliculus neurons to stimulation of the lateral lemniscus dorsal nucleus

The γ-aminobutyric acid neurons（GABAergic neurons） in the inferior colliculus are classified into various patterns based on their intrinsic electrical properties to a constant current injection. Although this classification is associated with physiological function, the exact role for neurons with various firing patterns in acoustic processing remains poorly understood. In the present study, we analyzed characteristics of inferior colliculus neurons in vitro, and recorded responses to stimulation of the dorsal nucleus of the lateral lemniscus using the wholecell patch clamp technique. Seven inferior colliculus neurons were tested and were classified into two firing patterns： sustained-regular（n = 4） and sustained-adapting firing patterns（n = 3）. The majority of inferior colliculus neurons exhibited slight changes in response to stimulation and bicuculline. The responses of one neuron with a sustained-adapting firing pattern were suppressed after stimulation, but recovered to normal levels following application of the γ-aminobutyric acid receptor antagonist. One neuron with a sustained-regular pattern showed suppressed stimulation responses, which were not affected by bicuculline. Results suggest that GABAergic neurons in the inferior colliculus exhibit sustained-regular or sustained-adapting firing patterns. Additionally, GABAergic projections from the dorsal nucleus of the lateral lemniscus to the inferior colliculus are associated with sound localization. The different neuronal responses of various firing patterns suggest a role in sound localization. A better understanding of these mechanisms and functions will provide better clinical treatment paradigms for hearing deficiencies.

A comparison of the spontaneous firing patterns between principal cells and fast spiking interneurons from dentate gyrus in waking guinea pigs

Objective To explore the possible mechanisms that cause the dentate gyrus （DG） neurons to play different roles in information coding. Methods In vivo extracellular single unit recording was performed on 22 waking female guinea pigs, which were positioned in a sound-attenuated recording chamber without any muscular relaxants. The spontaneous firing patterns of the DG neurons were detected and compared. Results There were two different electrophysiologi- cal populations in the DG of guinea pigs, principal cells （PCs） and fast spiking interneurons （INs）. Of the PCs, 1.3% discharged regularly, 48.1% irregularly and 50.6% in bursts ; in contrast, of the INs units, 64.1% discharged regularly, 2.6% irregularly and 33.3% in bursts. The spontaneous firing patterns of PCs were significantly different from those of INs （P 〈0.01 ）. In addition, the differences of several interspike interval （ISI） parameters also have been observed： （1） the ISI coefficients of variation of PCs （3.39 ± 3.56） were significantly higher than those of INs （1.08 ± 0.46） （P 〈0.01） ; （2） the ISI asymmetric indexes of PCs （0. 047±0. 059） were significantly lower than those of INs （0.569±0. 238） （P 〈 0.01 ）. Conclusion In the DG, the spontaneous firing patterns of PCs were significantly different from those of INs. The former were prone to fire in bursts, the latter were prone to fire regularly. The different roles in information coding between PCs and INs might be caused by their different firing patterns.

Potassium-induced bifurcations and chaos of firing patterns observed from biological experiment on a neural pacemaker

Changes of neural firing patterns and transitions between firing patterns induced by the introduction of external stimulation or adjustment of biological parameter have been demonstrated to play key roles in information coding.In this paper,bifurcation processes of bursting patterns were observed from an experimental neural pacemaker,through the adjustment of potassium parameter including ion concentration and calcium-dependent channel conductance.The adjustment of calcium-dependent potassium channel conductance was achieved by changing the extracellular tetraethylammonium concentration.The deterministic dynamics of chaotic bursting patterns induced by period-doubling bifurcation and intermittency,and lying between two periodic bursting patterns in a period-adding bifurcation process was investigated with a nonlinear prediction method.The bifurcations included period-doubling and period-adding bifurcations of bursting patterns.The experimental bifurcations and chaos closely matched those previously simulated in the theoretical neuronal model by adjusting potassium parameter,which demonstrated the simulation results of the theoretical model.The experimental results indicate that the potassium concentration and conductance of calcium-dependent potassium channel can induce bifurcations of the neural firing patterns.The potential role of these bifurcation structures in neural information coding mechanism is discussed.

Firing dynamics of an autaptic neuron

Autapses are synapses that connect a neuron to itself in the nervous system. Previously, both experimental and theoretical studies have demonstrated that autaptic connections in the nervous system have a significant physiological function. Autapses in nature provide self-delayed feedback, thus introducing an additional timescale to neuronal activities and causing many dynamic behaviors in neurons. Recently, theoretical studies have revealed that an autapse provides a control option for adjusting the response of a neuron： e.g., an autaptic connection can cause the electrical activities of the Hindmarsh–Rose neuron to switch between quiescent, periodic, and chaotic firing patterns; an autapse can enhance or suppress the mode-locking status of a neuron injected with sinusoidal current; and the firing frequency and interspike interval distributions of the response spike train can also be modified by the autapse. In this paper, we review recent studies that showed how an autapse affects the response of a single neuron.

Spiking patterns of a hippocampus model in electric fields

We develop a model of CA3 neurons embedded in a resistive array to mimic the effects of electric fields from a new perspective. Effects of DC and sinusoidal electric fields on firing patterns in CA3 neurons are investigated in this study. The firing patterns can be switched from no firing pattern to burst or from burst to fast periodic firing pattern with the increase of DC electric field intensity. It is also found that the firing activities are sensitive to the frequency and amplitude of the sinusoidal electric field. Different phase-locking states and chaotic firing regions are observed in the parameter space of frequency and amplitude. These findings are qualitatively in accordance with the results of relevant experimental and numerical studies. It is implied that the external or endogenous electric field can modulate the neural code in the brain. Furthermore, it is helpful to develop control strategies based on electric fields to control neural diseases such as epilepsy.

Control of firing activities in thermosensitive neuron by activating excitatory autapse

Temperature has distinct influence on the activation of ion channels and the excitability of neurons,and careful change in temperature can induce possible mode transition in the neural activities.The formation and development of autapse connection to neuron can enhance its self-adaption to external stimulus,and thus the firing patterns in neuron can be controlled effectively.The autapse is activated to drive a thermosensitive neuron,which is developed from the FitzHugh-Nagumo neural circuit by incorporating a thermistor,and the dynamics in the neural activities is explored to find mode dependence on the temperature and autaptic current.It is found that the firing modes can be controlled by temperature,and the neuron is wakened from resting state to periodic oscillation with the increase of temperature.Furthermore,the intensity and the intrinsic time delay in the autapse are respectively adjusted to control the neural activities,and it is confirmed that appropriate setting for autaptic current can balance and enhance the temperature effect on the neural activities.

Acoustic signal characteristic detection by neurons in ventral nucleus of the lateral lemniscus in mice

Under free field conditions, we used single unit extracellular recording to study the detection of acoustic signals by neurons in the ventral nucleus of the lateral lemniscus(VNLL) in Kunming mouse(Mus musculus). The results indicate two types of firing patterns in VNLL neurons: onset and sustained. The first spike latency(FSL) of onset neurons was shorter than that of sustained neurons. With increasing sound intensity, the FSL of onset neurons remained stable and that of sustained neurons was shortened, indicating that onset neurons are characterized by precise timing. By comparing the values of Q10 and Q30 of the frequency tuning curve, no differences between onset and sustained neurons were found, suggesting that firing pattern and frequency tuning are not correlated. Among the three types of rate-intensity function(RIF) found in VNLL neurons, the proportion of monotonic RIF is the largest, followed by saturated RIF, and non-monotonic RIF. The dynamic range(DR) in onset neurons was shorter than in sustained neurons, indicating different capabilities in intensity tuning of different firing patterns and that these differences are correlated with the type of RIF. Our results also show that the best frequency of VNLL neurons was negatively correlated with depth, supporting the view point that the VNLL has frequency topologic organization.

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.

Traveling chimera states in locally coupled memristive Hindmarsh-Rose neuronal networks and circuit simulation

Chimera states have been found in many physiology systems as well as nervous systems and may relate to neural information processing. The present work investigates the traveling chimera states in memristive neuronal networks of locally coupled Hindmarsh-Rose neurons, with both excitation and inhibition considered. Various traveling chimera patterns and firing modes are found to exist in the networks. Particularly, for excitatory connection, two kinds of traveling chimera states appear in opposite directions. Besides, a new type of chimera state composed of traveling chimera state and incoherent state is observed, named the semi-traveling chimera state. Multi-head traveling chimera states with several incoherent groups are also observed. For excitatory-inhibitory connection, the network is observed to exhibit an imperfect coherent state under the synergistic effect of strong excitatory and weak inhibitory coupling. Moreover, a firing pattern named mixed-amplitude bursting state is witnessed,consisting of two bursts of different amplitudes in a time sequence. Furthermore, an electric circuit is designed and built on Multisim to realize the above phenomena, suggesting that traveling chimera states could be generated in real circuits. Our findings can deepen the understanding of the electromagnetic induction effect in regulating the dynamics of neuronal networks and may provide useful clues for constructing artificial neural systems.

Synchronization and bursting transition of the coupled Hindmarsh-Rose systems with asymmetrical time-delays

The study of synchronization and bursting transition is very important and valuable in cognitive activities and action control of brain as well as enhancement for the reliability of the cortex synapses. However, we wonder how the synaptic strength and synaptic delay, especially the asymmetrical time-delays between different neurons can collectively influence their synchronous firing behaviors. In this paper, based on the Hindmarsh-Rose neuronal systems with asymmetrical time-delays, we investigate the collective effects of various delays and coupling strengths on the synchronization and bursting transition. It is shown that the interplay between delay and coupling strength can not only enhance or destroy the synchronizations but also can induce the regular transitions of bursting firing patterns. Specifically, as the coupling strength or time-delay increasing, the firing patterns of the time-delayed coupling neuronal systems consistently present a regular transition, that is, the periods of spikes during the bursting firings increase firstly and then decrease slowly. In particular, in contrast to the case of symmetrical time-delays,asymmetrical time-delays can lead to the paroxysmal synchronizations of coupling neuronal systems, as well as the concentration level of synchronization for the non-identically coupled system is superior to the one of identical coupling. These results more comprehensively reveal the rich nonlinear dynamical behaviors of neuronal systems and may be helpful for us to have a better understanding of the neural coding.