Narrow Results

The influences of phase noise together with autapse on the resonance dynamics in a modified FitzHugh–Nagumo (FHN) neuron are investigated by numerical simulation, where the neuronal model is in the environment of electromagnetic induction. First, it is found that phase noise can induce double coherence resonances, which is further confirmed to be robust to the feedback gain of induction current. Surprisingly, by individually changing the period of phase noise and the feedback gain, a resonance-like behavior also appears. Subsequently, the significant phenomenon of autapse-induced multiple coherence resonances is discovered. Moreover, the phenomenon of multiple coherence resonances can emerge at a broad parameter range of autaptic strength and autaptic delay.

This paper primarily investigates the inverse stochastic resonance (ISR) of neuron network driven by Lévy noise with electrical autapse and chemical autapse, respectively. Firstly, the discharge of Hodgkin–Huxley (HH) neuron network under different noise parameters, autapse parameters and network coupling strength is shown. Then, the variation of average firing rate with Lévy noise in the case of electrical autapse and chemical autapse is presented. We find that there exists a minimum value of the average firing rate curve caused by stability index and noise intensity of Lévy noise across the whole network, which is the phenomenon of ISR. With the increase of autaptic intensity and coupling strength, the ISR inhibitory effect of neuron discharge is weakened. In addition, with the increase of coupling strength, the neuron discharge of neural network is more intense and regular. As a consequence, our work suggests that autaptic intensity and coupling efficient of neuronal network can regulate the neuronal firing activities and suppress the effect of ISR, and Lévy noise can induce ISR phenomenon in Newman–Watts neuronal network.

Recently, neurobiologists have discovered axons on neurons which synapse on the same neuron's dendrites — so-called autapses. It is not yet clear what functional significance autapses offer for neural behavior. This is an ideal case for using a physical simulation to investigate how an autapse alters the firing of a neuron. We simulated a neural basket cell via the Hodgkin–Huxley equations and implemented an autapse which feeds back onto the soma of the neuron. The behavior of the cell was compared with and without autaptic feedback. Our artificial autapse neuron (AAN) displays oscillatory behavior which is not observed for the same model neuron without autapse. The neuron oscillates between two functional states: one where it fires at high frequency and another where firing is suppressed. This behavior is called "spike bursting" and represents a common pattern recorded from cerebral neurons.

Neuron models are available for computational neurodynamics and the main dynamical properties can be reproduced in the numerical scheme for further dynamical analysis. During model setting, some important biophysical factors should be considered and thus reliable neuron models can be approached. In this paper, a neuron model driven by autapse connection is investigated with the effect of electromagnetic induction being considered as well. A digital neuronal circuit is designed by using FPGA, the dynamical response and biological function of autapse connection. It is found that positive feedback in autapse can modulate the oscillating behaviors in the digital circuit, which could be effective for further investigation on digital neuronal network.

One-parameter and two-parameter bifurcations of the Morris–Lecar (ML) neuron model with and without the fast inhibitory autapse, which is a synapse from a neuron onto itself, are investigated. The ML neuron model without autapse manifests an inverse Hopf bifurcation point from firing to a depolarized resting state with high level of membrane potential, with increasing depolarization current. When a fast inhibitory autapse is introduced, a negative feedback or inhibitory current is applied to the ML model. With increasing conductance of the autapse to middle level, the depolarized resting state near the inverse Hopf bifurcation point can change to oscillation and the parameter region of the oscillation becomes wide, which can be well interpreted by the dynamic responses of the depolarized resting state to the inhibitory current stimulus mediated by the autapse. The enlargement of the parameter region of the oscillation induced by the negative feedback presents a novel viewpoint different from the traditional one that inhibitory synapse often suppresses the neuronal oscillation activities. Furthermore, complex nonlinear dynamics such as the coexisting behaviors and codimension-2 bifurcations including the Bautin and cusp bifurcations are acquired. The relationship between the bifurcations and the depolarization block, a physiological concept that indicates a neuron can enter resting state when receiving the depolarization current, is discussed.

This paper focuses on the dynamic behaviors of delay-coupled networks consisting of an arbitrary number of nonidentical neurons with unidirectional connections and an electrical synapse from one neuron onto itself. The stability criteria and different types of bifurcations are discussed by decomposing and analyzing the associated characteristic equation. Then, the study turns to the validation of theoretical results through numerical simulations and various interesting neural activities are observed, such as nontrivial equilibria, different patterns of oscillations, multistability coexistence, multiple switches between the quiescent and different periodic states, and transitions between the coexisting equilibria and the coexistence of equilibria and periodic oscillations. It is shown that time delays play important roles in the system performance and can be used to control neural activities.

It is important for functional neurons of animals or human beings to adapt to external stimuli, such as sound, pressure, and light. Regarding this aspect, autaptic neuron enables itself to utilize historical information to modulate its instant dynamics, such that it may be able to behave adaptively. In this paper, a FitzHugh–Nagumo based autaptic neuron is employed to investigate the capability of a sound-sensitive neural circuit’s adaptation and filtering to analog acoustic signals. Extensive simulations are performed for excitatory and inhibitory types of autaptic neurons. The results show that the time-delayed feedback of the excitatory chemical autapse can be tuned to play the role of a narrow-band filter in response to a broadband acoustic signal. While the excitatory chemical autaptic neuron cannot saturate its response amplitude due to its positive feedback gain, the inhibitory chemical autapse can drive the neuron’s amplitude to converge as the intensity of external drive increases, which reveals the capability of adaptation. What’s more, the inhibitory chemical autaptic neuron can also exhibit a novel bursting adaptation, in which the number of spikings contained in one bursting changes as the electrical activity evolves. For electrical autaptic neurons, it is also found that both time-delay feedback gains can effectively modulate the response of neuron to acoustic signal. While the variation of time-lags mainly changes the spiking rates of the excitatory electrical autaptic neuron, the feedback gain alters its response amplitude. Lastly, by carefully tuning the time-lags, the expected subthreshold dynamics for larger inhibitory feedback gains can be switched to nearby quasi-periodic firings, which implies a competing relation between the time-delays and the feedback gains in the spiking dynamics of the inhibitory electrical autaptic neurons. The diverse emerging phenomena are expected to facilitate the design of online or interactive learning artificial neural networks with these functional autaptic neurons.

In this paper, we study analytically the impact of an inhibitory autapse on neuronal activity. In order to do this, we formulate conditions on a set of non-adaptive spiking neuron models with delayed feedback inhibition, instead of considering a particular neuronal model. The neuron is stimulated with a stochastic point renewal process of excitatory impulses. Probability density function (PDF) $p(t)$ of output interspike intervals (ISIs) of such a neuron is found exactly without any approximations made. It is expressed in terms of ISIs PDF for the input renewal stream and ISIs PDF for that same neuron without any feedback. Obtained results are applied to a subset of neuronal models with threshold 2 when the time intervals between input impulses are distributed according to the Erlang-2 distribution. In that case, we have found explicitly the model-independent initial part of ISIs PDF $p(t)$ defined at some initial interval $[0;T_2]$ of ISI values.