Nagumo Neurons Research Articles

Mechanism of Selectivity in the Coupled FitzHugh – Nagumo Neurons

Mechanism of Selectivity in the Coupled FitzHugh – Nagumo Neurons

Self-organization collective dynamics of heterogeneous neurons with memristive and plastic chemical synapses

Hybrid synapses widely exist in the brain neural system, but how memristive and plastic chemical synapses cooperatively modulate the collective dynamics of neurons remains largely unknown. Here, we constructed self-organized networks with two heterogeneous FitzHugh–Nagumo (FHN) neurons coupled with memristive and chemical synapses, wherein the chemical synapse is modulated by the spike-timing-dependent plasticity (STDP) rule. Additionally, three kinds of network models involving excitatory–excitatory ([Formula: see text]–[Formula: see text] neurons, high excitatory–inhibitory (high [Formula: see text]–[Formula: see text]) neurons and low excitatory–inhibitory (low [Formula: see text]–[Formula: see text]) neurons were constructed. The modulation of memristive synapses on the structure and dynamics of self-organized neuronal networks is greatly dependent on model selection. Stronger coupling of memristive synapses induces consistently more stable network structure and enhanced network synchronization in the [Formula: see text]–[Formula: see text] and high [Formula: see text]–[Formula: see text] models but has complex effects on the low [Formula: see text]–[Formula: see text] neuronal network. In contrast, increasing the closing rate of memristive synapses has little effect on the [Formula: see text]–[Formula: see text] and high [Formula: see text]–[Formula: see text] networks but can accelerate the self-organization process and result in more complex firing patterns and weaker synchronization in the low [Formula: see text]–[Formula: see text] network. These results provide further understanding of the mechanism of the self-organized neuronal network dynamics underlying hybrid synapses and neuronal excitation.

Ring generator of neuron-like activity with tunable frequency

The aim of the work is to build a radiophysical generator of neuron-like activity with a frequency tunable in various ways, corresponding to modern ideas about the structure of the hippocampus and the generation of pathological epileptic rhythms in it. Methods. The elements of the generator are radio engineering implementations of the complete FitzHugh– Nagumo neuron and the electronic implementation of a chemical synapse in the form of a sigmoid function with a delayed argument. The simulation was carried out in the SPICE simulator. Results. Various ways of introducing delay into the coupling are considered: an ideal delay line, a phase filter with a rheostat, one tunable Bessel filter, and a sequence of non-tunable Bessel filters. For circuit implementation, the approach using a Bessel filter with a rheostat is recognized as optimal as a compromise between simplicity and minimization of signal distortion. The dependences of the oscillation frequency on the number of elements in the ring and the delay time are constructed. The bistability of generation regimes is studied for certain values of the parameters. The effect of inclusion of inhibitory elements (interneurons) in the circuit is considered. Conclusion. The constructed ring generator models the experimentally observed properties of the dynamics of epileptic discharge fundamental frequency in limbic epilepsy. It is able to reproduce the occurrence of oscillations as a result of external short-term driving, smooth and sharp frequency tuning, the coexistence of different modes with the same parameters.

Clamping and Synchronization in the Strongly Coupled FitzHugh--Nagumo Model

We investigate the dynamics of a limit of interacting FitzHugh--Nagumo neurons in the regime of large interaction coefficients. We consider the dynamics described by a mean-field model given by a n...

Dynamic characteristics in two-dimensional FitzHugh–Nagumo neural system driven by Lévy noise

In this paper, the steady state characteristics and stochastic resonance (SR) in two-dimensional FitzHugh–Nagumo (FHN) neuron system driven by Lévy noise are studied. The system is simulated by Janicki–Weron algorithm and fourth-order Runge–Kutta method, and the steady state characteristics of the system are analyzed by stationary probability density (SPD) functions. Then, the SR is determined by the classical measure of signal-to-noise ratio (SNR). Through numerical simulation, it is found that the Lévy noise can induce the transition of the system. In addition, the effects of different parameters on the SR are analyzed by SNR.

Parameter Estimation of the FitzHugh–Nagumo Neuron Model Using Integrals Over Finite Time Periods

This paper proposes two methodologies for estimating the parameters of the FitzHugh–Nagumo (FHN) neuron model. The identification procedures use only measurements of the membrane potential. The first technique is named the identification method based on integrals and wavelets (IMIW), which combines a parameterization based on integrals over finite time periods and a wavelet denoising technique for removing the measurement noise. The second technique, termed as the identification method based only on integrals (IMOI), does not use any wavelet denoising technique and attenuates the measurement noise by integrating the IMIW parameterization two times more over finite time periods. Both procedures use the least squares algorithm for estimating the FHN parameters. Integrating the FHN model over finite time periods allows eliminating the unmeasurable recovery variable of this model, thus obtaining a parameterization based on integrals of the measurable membrane potential variable. Unlike an identification technique recently published, the proposed methods do not rely on the time derivatives of the membrane potential and are not limited to continuously differentiable input current stimulus. Numerical simulations show that both the IMIW and IMOI have a good and a similar performance, however, the implementation of the latter is simpler than the implementation of the former.

Neural Activity Measures and Their Dynamics

We provide an asymptotically justified derivation of activity measure evolution equations (AMEEs) for a finite size neural network. The approach takes into account the dynamics for each isolated neuron in the network being modeled by a biophysical model, i.e., Hodgkin--Huxley equations or their reductions. By representing the interacting network as self- and pairwise-interactions, we propose a general definition of spatial projections of the network, called activity measures, that quantify the activity of a network. We show that the evolution equations that govern the dynamics of the activity measure shadow the activity measure of the network (i.e., the two quantities stay close to each other for all times) for general interactions and various asymptotic dynamics. The AMEEs effectively serve as a dimensionality reduction technique for the complex network when spatial synchrony and coherence are present and allow us to a priori predict network dynamics that would not be guessed from individual neuron behavior. To demonstrate an explicit derivation of such a reduction, we consider the mean measure for a network of interacting FitzHugh--Nagumo neurons. Computational results comparing the full network dynamics with the mean AMEE model of identical and nonidentical FitzHugh--Nagumo and FitzHugh--Rinzel neurons validate the shadowing theorems and expose the various resulting AMEE models that allow us to describe the mean of the network.

Chaos synchronization of coupled neurons under external electrical stimulation using adaptive H∞ control

In this paper, H∞ control via an adaptive neural network approach is proposed to realize the synchronization of two gap junction coupled chaotic FitzHugh—Nagumo (FHN) neurons under external electrical stimulation. The control scheme is robust to the uncertainties such as unmodelled dynamics, ionic channel noise and external disturbances. Asymptotic chaos synchronization is obtained by proper choice of the control parameters. The simulation results demonstrate the effectiveness of the proposed control method.