FHN Neuron Research Articles

Phase synchronization under mixed synapse between two heterogeneous functional neurons

Nervous system contacts and regulates the various systems and organs of the body by encoding and transmitting information, so it becomes important to explore the synaptic connections between neurons. In this study, two functional neurons are obtained by embedding Josephson junction and memristor in the FHN neuron circuit, and then based on Helmholtz’s theorem their Hamilton energies are calculated and investigated when coupled channel is awakened. There are weak but stable and orderly electromagnetic fields around human tissues and organs due to the transmembrane flow of ions, and their equilibrium state is easily disturbed and destroyed by the external electromagnetic fields, which should be considered when neuron model are investigated. Thus, an induction coil and a charge-controlled memristor (CCM) are used to perceive magnetic and electric fields respectively to couple the two function neurons, then mixed synapse is activated and synaptic plasticity is detect by parameter modulation and energy exchange. It is found that energy is continuously pumped along the coupling channel even if the synaptic connection is increased further, and two different functional neurons can only achieve quasi-phase synchronization or phase lock. However, the coupling strength threshold for achieving quasi-phase synchronization is lowered under hybrid synapses, and the possible mechanism may be that the addition of induction coil and CCM can induce time-varying electric and magnetic fields, which in turn facilitate the energy exchange in the coupled system. This study not only helps us to reveal the synchronization phenomenon of certain neurons observed in experiments, but also to explain the occurrence of pathological synchronization in the nervous system.

Recurrence quantification and bifurcation analysis of electrical activity in resistive/memristive synapse coupled Fitzhugh–Nagumo type neurons

Temporal response of excitable individual and coupled different neuronal circuits i.e., Cell-I and Cell-II, of Fitzhugh–Nagumo type have been numerically simulated with a view to understand and characterize the complexities of involved dynamical processes. FHN neuronal circuit Cell-I and Cell-II have been shown to exhibit supercritical Hopf bifurcation, when excited by an external steady stimulus. For time varying sinusoidal excitation, the temporal action potential behavior of these neuronal circuits, when analyzed using measures of recurrence quantification analysis (RQA) and bifurcation diagram reveals period-1, period-2, multi-periodic, chaotic and reverse period doubling characteristics as observed earlier experimentally in giant squid axon and other biological cell assemblies. Phase portrait, bifurcation diagrams and recurrence plot (RPs), of (i) unidirectional and (ii) bidirectional coupled FHN Cell-I and Cell-II, through a gap junction resistor, suggest the possibility of transition to intermittent state besides the transition of respective action potential from periodic to multi-periodic to chaotic state in an ordered or disordered fashion, depending on values of system parameters that control the complexities. Further, for both the configurations (i) and (ii), synchronization of FHN neuron Cell-I with Cell-II is also shown to occur for large values of coupling parameter, ξ. The dynamical effect of electromagnetic radiation on individual FHN neuron circuits has also been investigated using a flux controlled memristor that couples the magnetic flux with the individual FHN neurons. Phase portrait, bifurcation and RQA analysis have also been used to characterize the electrical activities of excitable cell assemblies involving memristive synapse coupled FHN neuronal Cell-I and Cell-II in settings (i) and (ii) respectively.

Stability and Hopf bifurcation of FHN neuron model with time delay under magnetic flow

Stability and Hopf bifurcation of FHN neuron model with time delay under magnetic flow

Theory and Application of Weak Signal Detection Based on Stochastic Resonance Mechanism

Stochastic resonance is a new type of weak signal detection method. Compared with traditional noise suppression technology, stochastic resonance uses noise to enhance weak signal information, and there is a mechanism for the transfer of noise energy to signal energy. The purpose of this paper is to study the theory and application of weak signal detection based on stochastic resonance mechanism. This paper studies the stochastic resonance characteristics of the bistable circuit and conducts an experimental simulation of its circuit in the Multisim simulation environment. It is verified that the bistable circuit can achieve the stochastic resonance function very well, and it provides strong support for the actual production of the bistable circuit. This paper studies the stochastic resonance phenomenon of FHN neuron model and bistable model, analyzes the response of periodic signals and nonperiodic signals, verifies the effect of noise on stochastic resonance, and lays the foundation for subsequent experiments. It proposes to feedback the link and introduces a two-layer FHN neural network model to improve the weak signal detection performance under a variable noise background. The paper also proposes a multifault detection method based on the total empirical mode decomposition of sensitive intrinsic mode components with variable scale adaptive stochastic resonance. Using the weighted kurtosis index as the measurement index of the system output can not only maintain the similarity between the system output signal and the original signal but also be sensitive to impact characteristics, overcoming the missed or false detection of the traditional kurtosis index. Experimental research shows that this method has better noise suppression ability and a clear reproduction effect on details. Especially for images contaminated by strong noise (D = 500), compared with traditional restoration methods, it has better performance in subjective visual effects and signal-to-noise ratio evaluation.

Dynamical Complexity of FHN Neuron System Driven by Correlated Noises and Periodic Signal

In this paper, the dynamical complexity of FHN neuron system under the co-excitation of correlated noises and periodic signals is studied by means of information theory measures. Based on the definition of statistical complexity and normalized Shannon entropy, as well as the Bandt–Pompe algorithm, the total statistical complexity and the total normalized Shannon entropy of the FHN neuron system are calculated. Because the potential function of the system is asymmetric, we also calculate the statistical complexity and the normalized Shannon entropy in two different potential wells respectively. Moreover, the effects of additive noise intensity, multiplicative noise intensity, noise correlation time, cross-correlation strength and amplitude on dynamical complexity are analyzed.

Phase coupling synchronization of FHN neurons connected by a Josephson junction

A variety of nonlinear circuits can be tamed to reproduce the main dynamical properties in neural activities for biological neurons while designing reliable artificial synapses for connecting these neural circuits becomes a challenge. In this paper, a Josephson junction is used to build coupling channel for connecting two FitzHugh-Nagumo neural circuits driven by periodical voltage source. The hybrid synapse is designed by using a linear resistor paralleled with a Josephson junction, which can estimate the effect of external magnetic field by generating additive phase error between the junction. Indeed, it activates nonlinear coupling due to phase diversity in the Josephson junction. The coupled circuits are estimated in dimensionless dynamical systems by applying scale transformation on the variables and parameters in neural circuits. In fact, the intrinsic parameters of coupling channel are adjusted to detect the occurrence of synchronization. Bifurcation analysis is calculated to predict and confirm the occurrence of synchronization between two neural circuits. It is found that synchronization can be stabilized between two FHN neural circuits by selecting appropriate values for parameters in the Josephson junction involved in the coupling channel. It gives useful guidance for implementing artificial synapse for signal processing in neural circuits.

Multiplierless Digital Implementation of Time-Varying FitzHugh–Nagumo Model

Low-cost accurate digital realization of the spiking neural networks is crucial to investigate the behaviors of human brain performance. This paper presents a multiplierless burst-mode Fitz–Hugh Nagumo (MBM-FHN) model, which is used for generating the burst-mode of the FHN neuron model. Using extra parameters (time-varying function) in neuron equations and estimating it by linear function, efficient low-cost and high-speed implementation is achieved. The simulation results show that the MBM-FHN model generates the similar bursting patterns of the original FHN neuron. The comparison shows that the MBM-FHN model has a better performance and best cost reduction related to the original neuron model especially in overall saving and speed-up parameters.

Stochastic multiresonance in coupled excitable FHN neurons.

In this paper, effects of noise on Watts-Strogatz small-world neuronal networks, which are stimulated by a subthreshold signal, have been investigated. With the numerical simulations, it is surprisingly found that there exist several optimal noise intensities at which the subthreshold signal can be detected efficiently. This indicates the occurrence of stochastic multiresonance in the studied neuronal networks. Moreover, it is revealed that the occurrence of stochastic multiresonance has close relationship with the period of subthreshold signal Te and the noise-induced mean period of the neuronal networks T0. In detail, we find that noise could induce the neuronal networks to generate stochastic resonance for M times if Te is not very large and falls into the interval (M×T0,(M+1)×T0) with M being a positive integer. In real neuronal system, subthreshold signal detection is very meaningful. Thus, the obtained results in this paper could give some important implications on detecting subthreshold signal and propagating neuronal information in neuronal systems.

Systematic Computation of Nonlinear Bilateral Dynamical Systems With a Novel Low-Power Log-Domain Circuit

Simulation of large-scale nonlinear dynamical systems on hardware with a high resemblance to their mathematical equivalents has been always a challenge in engineering. This paper presents a novel current-input current-output circuit supporting a systematic synthesis procedure of log-domain circuits capable of computing bilateral dynamical systems with considerably low power consumption and acceptable precision. Here, the application of the method is demonstrated by synthesizing four different case studies: 1) a relatively complex 2-D nonlinear neuron model; 2) a chaotic 3-D nonlinear dynamical system Lorenz attractor having arbitrary solutions for certain parameters; 3) a 2-D nonlinear Hopf oscillator, including bistability phenomenon sensitive to initial values; and 4) three small neurosynaptic networks comprising three FHN neuron models variously coupled with excitatory and inhibitory synapses. The validity of our approach is verified by nominal and Monte Carlo simulated results with realistic process parameters from the commercially available AMS 0.35- $\mu \text{m}$ technology. The resulting continuous-time, continuous-value, and low-power circuits exhibit various bifurcation phenomena, nominal time-domain responses in good agreement with their mathematical counterparts and fairly acceptable process variation results (less than 5% STD).

Bifurcation structure of two coupled FHN neurons with delay

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh–Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich. The neural system exhibits a unique rest point or three ones for the different values of coupling strength by employing the pitchfork bifurcation of non-trivial rest point. The asymptotic stability and possible Hopf bifurcations of the trivial rest point are studied by analyzing the corresponding characteristic equation. Homoclinic, fold, and pitchfork bifurcations of limit cycles are found. The delay-dependent stability regions are illustrated in the parameter plane, through which the double-Hopf bifurcation points can be obtained from the intersection points of two branches of Hopf bifurcation. The dynamical behavior of the system may exhibit one, two, or three different periodic solutions due to pitchfork cycle and torus bifurcations (Neimark–Sacker bifurcation in the Poincare map of a limit cycle), of which detection was impossible without exact and systematic dynamical study. In addition, Hopf, double-Hopf, and torus bifurcations of the non trivial rest points are found. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behaviors are clarified.

Parameter dependence of stochastic resonance in the FitzHugh-Nagumo neuron model driven by trichotomous noise

We investigate the stochastic resonance in a FitzHugh-Nagumo neuron model driven by trichotomous noise and periodic signal, focusing on the dependence of properties of stochastic resonance (SR) on system parameters. The stochastic resonance is shown through several different measures: system response, power spectrum and signal-to-noise ratio. Firstly, it is found that whether the neuron can fire regularly depends on the cooperative effect of the signal frequency and the signal amplitude for the deterministic FHN neuron. When the forcing amplitude alone is insufficient to cause the neuron firing, the neuron can fire with the addition of trichotomous noise. Secondly, we show that power spectrum is maximized for an optimal value of the noise correlation time, which is the signature of SR. Finally, from studying SNR, the specific system parameters are found to optimize the SR phenomenon.

Impulsive synchronization seeking in general complex delayed dynamical networks

The present paper investigates the issues of impulsive synchronization seeking in general complex delayed dynamical networks with nonsymmetrical coupling. By establishing the extended Halanay differential inequality on impulsive delayed dynamical systems, some simple yet generic sufficient conditions for global exponential synchronization of the impulsive controlled delayed dynamical networks are derived analytically. Compared with some existing works, the distinctive features of these sufficient conditions indicate two aspects: on the one hand, these sufficient conditions can provide an effective impulsive control scheme to synchronize an arbitrary given delayed dynamical network to a desired synchronization state even if the original given network may be asynchronous itself. On the other hand, the controlled synchronization state can be selected as a weighted average of all the states in the network for the purpose of practical control strategy, which reveals the contributions and influences of various nodes in synchronization seeking processes of the dynamical networks. It is shown that impulses play an important role in making the delayed dynamical networks globally exponentially synchronized. Furthermore, the results are applied to a typical nearest-neighbor unidirectional time-delay coupled networks composed of chaotic FHN neuron oscillators, and numerical simulations are given to demonstrate the effectiveness of the proposed control methodology.

Hopf bifurcation analysis in a synaptically coupled FHN neuron model with delays

This paper presents an investigation of stability and Hopf bifurcation of the synaptically coupled nonidentical FHN model with two time delays. We first consider the existence of local Hopf bifurcations, by regarding the sum of the two delays as a parameter, then derive explicit formulas for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions, using the normal form method and center manifold theory. Finally, numerical simulations are carried out for supporting the theoretical analysis.

Global synchronization in general complex delayed dynamical networks and its applications

The main objective of the present paper is further to investigate global synchronization of a general model of complex delayed dynamical networks. Based on stability theory on delayed dynamical systems, some simple yet less conservative criteria for both delay-independent and delay-dependent global synchronization of the networks are derived analytically. It is shown that under some conditions, if the uncoupled dynamical node is stable itself, then the network can be globally synchronized for any coupling delays as long as the coupling strength is small enough. On the other hand, if each dynamical node of the network is chaotic, then global synchronization of the networks is heavily dependent on the effects of coupling delays in addition to the connection configuration. Furthermore, the results are applied to some typical small-world (SW) and scale-free (SF) complex networks composing of coupled dynamical nodes such as the cellular neural networks (CNNs) and the chaotic FHN neuron oscillators, and numerical simulations are given to verify and also visualize the theoretical results.

The role of synaptic coupling in a network of FHN neuron models

The role of synaptic coupling in a network of FHN neuron models