Phase synchronization between a light-dependent neuron and a thermosensitive neuron

Wave propagation in a light-temperature neural network under adaptive local energy balance

External electric and mechanical stimuli can induce shape deformation in excitable media because of its intrinsic flexible property. When the signals propagation in the media is described by a neural network, creation of heterogeneity or defect is considered as the effect of shape deformation due to accumulation or release of energy in the media. In this paper, a temperature-light sensitive neuron model is developed from a nonlinear circuit composed of a phototube and a thermistor, and the physical energy is kept in capacitive and inductive terms. Furthermore, the Hamilton energy for this function neuron is obtained in theoretical way. A regular neural network is built on a square array by activating electric synapse between adjacent neurons, and a few of neurons in local area is excited by noisy disturbance, which induces local energy diversity, and continuous coupling enables energy propagation and diffusion. Initially, the Hamilton energy function for a temperature-light sensitive neuron can be obtained. Then, the finite neurons are applied noise to obtain energy diversity to explore the energy spread between neurons in the network. For keeping local energy balance, one intrinsic parameter is regulated adaptively until energy diversity in this local area is decreased greatly. Regular pattern formation indicates that local energy balance creates heterogeneity or defects and a few of neurons show continuous parameter shift for keeping energy balance in a local area, which supports gradient energy distribution for propagating waves in the network.

A neuron model with nonlinear membranes

One-layer membrane separates the gradient field in and out of the cell, while some two-layer membranes filled with excitable media/material are important to regulate the energy flow when ions are propagated and diffused. The intracellular and extracellular media can be effectively separated by the membrane. It is important to clarify and describe the biophysical function and then the capacitive property can be reproduced in equivalent neural circuit. Here, we suggest the cell membrane has certain thickness and becomes flexible under external stimuli, therefore, it is considered as a kind of nonlinear media. To mimic the physical property of the two-layer cell membrane, a nonlinear resistor is used to connect two linear circuits, which is used to describe the electrical characteristic of two sides of the cell membrane, respectively. The combination of two linear circuits via a nonlinear resistor can describe the energy characteristic and firing mode in the flexible membrane of biophysical neurons. Circuit equations are defined and converted into equivalent nonlinear oscillator like a neuron. The voltage difference for the two capacitors can be consistent with the membrane potential for the neuron. The Hamilton energy function for this neuron can be mapped from the field energy in the electronic components, and it is also derived by using Helmholtz's theorem. The neuron can show similar spiking and bursting firing patterns, and uncertain diversity in membrane potentials is effective to support continuous firing patterns and mode transition under external stimulus. Furthermore, noisy disturbance is applied to induce coherence resonance. The results indicate that the lower coefficient variability and higher average energy level supports periodic firing in the neuron under coherence resonance. Therefore, this neuron model with nonlinear membranes (or two-layer form) is more suitable for identifying the biophysical property of biological neuron.

A Josephson junction-coupled neuron with double capacitive membranes

The channel currents have distinct magnetic field effect and any changes of the electromagnetic field or electirc stimulus will change the membrane potential effectively. A feasible neuron model considers the distinct physical characteristic is more suitable to mimic the neural activities accompanying with shift in energy level. A Josephson junction (JJ) is connected to a neural circuit for estimating the effect of external magnetic field and two capacitors are connected via a linear resistor for mimicing the capacitive field beside two sides of the cell membrane. Its equivalent Hamilton energy is calculated to show the relation between firing mode and energy level. Noisy disturbance is imposed to predict the occurrence of coherence resonance, and the biophysical neuron is excited to present higher energy level. This new neuron model can address the field effect and the biophysical property of cell membrane considered as combination of capacitive fields in double capacitors. It can mimic the physical property of outer and inner membranes, and energy exchange across the double membranes explains the energy mechanism in neural activities. Time-varying energy diveristy between capacitive field is crucial for supporting continuous firing activities. The JJ channel discerns slight changes in external magnetic field and regularity is stabilized under coherence resonance in presence of noisy excitation on the membrane or ion channels.

Almost periodic quasi-projective synchronization of delayed fractional-order quaternion-valued neural networks

This paper examines the issue of almost periodic quasi-projective synchronization of delayed fractional-order quaternion-valued neural networks. First, using a direct method rather than decomposing the fractional quaternion-valued system into four equivalent fractional real-valued systems, using Banach's fixed point theorem, according to the basic properties of fractional calculus and some inequality methods, we obtain that there is a unique almost periodic solution for this class of neural network with some sufficient conditions. Next, by constructing a suitable Lyapunov functional, using the characteristic of the Mittag-Leffler function and the scaling idea of the inequality, the adequate conditions for the quasi-projective synchronization of the established model are derived, and the upper bound of the systematic error is estimated. Finally, further use Matlab is used to carry out two numerical simulations to prove the results of theoretical analysis.

Hamilton energy balance and synchronization behaviors of two functional neurons

The nervous system is composed of various functional neurons, some of which perceive sound or light, and these physical signals can be converted into bioelectrical signals. From the biophysical point of view, piezoelectric ceramic embedded in neuronal circuits can detect the external auditory waves, while phototube can capture light signals, so as to obtain two functional neurons with auditory recognition and light-dependent recognition. Considering the two identical or different functional neurons are connected by an induction coil to stimulate magnetic field coupling, and there will be energy diversity when they are driven by different initial conditions or external stimulation. Thus, synaptic connections can be activated and awakened in an adaptive manner when field energy is exchanged, and the coupling channel remains open until the energy diversity between neurons is controlled at a limited threshold. For this purpose, a criterion of the coupling strength increases exponentially is proposed to discuss the enhancement of neuronal synaptic connections. It is found that two neurons can be coupled adaptively to achieve complete synchronization, quasi-synchronization or intermittent quasi-synchronization. These results could help in designing functional assistive devices for patients with hearing or vision impairment.

Extreme multistability and phase synchronization in a heterogeneous bi-neuron Rulkov network with memristive electromagnetic induction

Memristive electromagnetic induction effect has been widely explored in bi-neuron network with homogeneous neurons, but rarely in bi-neuron network with heterogeneous ones. This paper builds a bi-neuron network by coupling heterogeneous Rulkov neurons with memristor and investigates the memristive electromagnetic induction effect. Theoretical analysis discloses that the bi-neuron network possesses a line equilibrium state and its stability depends on the memristor coupling strength and initial condition. That is, the stability of the line equilibrium state has a transition between unstable saddle-focus and stable node-focus via Hopf bifurcation. By employing parameters located in the stable node-focus region, dynamical behaviors related to the memristor coupling strength and initial conditions are revealed by Julia- and MATLAB-based multiple numerical tools. Numerical results demonstrate that the proposed heterogeneous bi-neuron Rulkov network can generate point attractor, period, chaos, chaos crisis, and period-doubling bifurcation. Note that extreme multistability are disclosed with respect to initial conditions of memristor and gated ion concentration. Coexisting infinitely multiple firing patterns of periodic firing patterns with different periodicities and chaotic firing patterns for different memristor initial conditions are demonstrated by phase portrait and time-domain waveform. Besides, the phase synchronization related to the memristor coupling strength and its initial condition is explored, which suggests that the two heterogeneous neurons become phase synchronization with large memristor coupling strength and initial condition. This also reflects that the plasticity of memristor synapse enables adaptive regulation in keeping energy balance between the neurons. What's more, MCU-based hardware experiments are executed to further confirm the numerical simulations.

Complex dynamics of hair bundle of auditory nervous system (II): forced oscillations related to two cases of steady state

The forced oscillations of hair bundle of inner hair cells of auditory nervous system evoked by external force from steady state are related to the fast adaption of hair cells, which are very important for auditory amplification. In the present paper, comprehensive and deep understandings to nonlinear dynamics of forced oscillations are acquired in four aspects. Firstly, the complex dynamics underlying the twitch (fast recoil of displacement X which is fast variable) induced from Case-1 and Case-2 steady states by external pulse force are obtained. With help of vector fields and nullclines, the phase trajectory of forced oscillations is identified to be an evolution process between two equilibrium points corresponding to zero force and pulse force, respectively, and then the twitch is obtained as the behavior running along the nonlinear part of X-nullcline. Especially, twitch observed in experiment are classified into 6 types, which are induced by negative change of force, negative and positive changes of force, and positive change of force, respectively, and further build relationships to three subcases of Case-2 steady state with N-shaped X-nullcline (equilibrium point locates on the left, middle, and right branches of X-nullcline, respectively). Secondly, the experimental observation of fatigue of twitch induced by continual two pulse forces, i.e. the reduced amplitude of the latter twitch when interval between two forces is short, is also explained as a nonlinear behavior beginning from an initial value different from that of the former one. Thirdly, the experimental observation of transition between sustained oscillations and steady state induced by pulse force can be simulated for Case-1 steady state with Z-shaped X-nullcline instead of Case-2, due to that there exists bifurcations with respect to external force for Case-1 while no bifurcations for Case-2. Last, the threshold phenomenon induced by simple pulse stimulation exists for Case-1 steady state rather than Case-2, due to that the upper and lower branches of Z-shaped X-nullcline close to the middle branch exhibit coexisting behaviors of variable X while N-shaped X-nullcline does not. The nonlinear dynamics of forced oscillations are helpful for explanations to the complex experimental observations, which presents potential measures to modulate the functions of twitch such as the fast adaption.

How to discern external acoustic waves in a piezoelectric neuron under noise?

Biological neurons keep sensitive to external stimuli and appropriate firing modes can be triggered to give effective response to external chemical and physical signals. A piezoelectric neural circuit can perceive external voice and nonlinear vibration by generating equivalent piezoelectric voltage, which can generate an equivalent trans-membrane current for inducing a variety of firing modes in the neural activities. Biological neurons can receive external stimuli from more ion channels and synapse synchronously, but the further encoding and priority in mode selection are competitive. In particular, noisy disturbance and electromagnetic radiation make it more difficult in signals identification and mode selection in the firing patterns of neurons driven by multi-channel signals. In this paper, two different periodic signals accompanied by noise are used to excite the piezoelectric neural circuit, and the signal processing in the piezoelectric neuron driven by acoustic waves under noise is reproduced and explained. The physical energy of the piezoelectric neural circuit and Hamilton energy in the neuron driven by mixed signals are calculated to explain the biophysical mechanism of auditory neuron when external stimuli are applied. It is found that the neuron prefers to respond to the external stimulus with higher physical energy and the signal which can increase the Hamilton energy of the neuron. For example, stronger inputs used to inject higher energy and it is detected and responded more sensitively. The involvement of noise is helpful to detect the external signal under stochastic resonance, and the additive noise changes the excitability of neuron as the external stimulus. The results indicate that energy controls the firing patterns and mode selection in neurons, and it provides clues to control the neural activities by injecting appropriate energy into the neurons and network.

A nonlinear memductance induced intermittent and anti-phase synchronization

We introduce a model to mimic the dynamics of oscillators that are coupled by mean-field nonlinear memductance. Notably, nonlinear memductance produces dynamic nonlinearity, which causes the direction of coupling to change over time. Depending on the parameters, such a dynamic coupling drives the trajectory of oscillators to a synchronization or anti-synchronization manifold. Specifically, depending on the forcing frequency and coupling strength, we find anti-phase and intermittent synchronization. With the increase in coupling magnitude, one can observe a transition from intermittent synchronization to complete synchronization through anti-phase synchronization. The results are validated through numerical simulations. The hypothesis has a huge impact on the study of neuronal networks.

Lag Synchronization of Noisy and Nonnoisy Multiple Neurobiological Coupled FitzHugh–Nagumo Networks with and without Delayed Coupling

This paper presents a methodology for synchronizing noisy and nonnoisy multiple coupled neurobiological FitzHugh–Nagumo (FHN) drive and slave neural networks with and without delayed coupling, under external electrical stimulation (EES), external disturbance, and variable parameters for each state of both FHN networks. Each network of neurons was configured by considering all aspects of real neurons communications in the brain, i.e., synapse and gap junctions. Novel adaptive control laws were developed and proposed that guarantee the synchronization of FHN neural networks in different configurations. The Lyapunov stability theory was utilized to analytically derive the sufficient conditions that ensure the synchronization of the FHN networks. The effectiveness and robustness of the proposed control laws were shown through different numerical simulations.

A novel hybrid soft computing optimization framework for dynamic economic dispatch problem of complex non-convex contiguous constrained machines

The reformations of the electrical power sector have resulted in very dynamic and competitive market that has changed many elements of the power industry. Excessive demand of energy, depleting the fossil fuel reserves of planet and releasing the toxic air pollutant, has been causing harm to earth habitats. In this new situation, insufficiency of energy supplies, rising power generating costs, high capital cost of renewable energy equipment, environmental concerns of wind power turbines, and ever-increasing demand for electrical energy need efficient economic dispatch. The objective function in practical economic dispatch (ED) problem is nonlinear and non-convex, with restricted equality and inequality constraints, and traditional optimization methods are incapable of resolving such non-convex problems. Over the recent decade, meta-heuristic optimization approaches have acquired enormous reputation for obtaining a solution strategy for such types of ED issues. In this paper, a novel soft computing optimization technique is proposed for solving the dynamic economic dispatch problem (DEDP) of complex non-convex machines with several constraints. Our premeditated framework employs the genetic algorithm (GA) as an initial optimizer and sequential quadratic programming (SQP) for the fine tuning of the pre-optimized run of GA. The simulation analysis of GA-SQP performs well by acquiring less computational cost and finite time of execution, while providing optimal generation of powers according to the targeted power demand and load, whereas subject to valve point loading effect (VPLE) and multiple fueling option (MFO) constraints. The adequacy of the presented strategy concerning accuracy, convergence as well as reliability is verified by employing it on ten benchmark case studies, including non-convex IEEE bus system at the same time also considering VPLE of thermal power plants. The potency of designed optimization seems more robust with fast convergence rate while evaluating the hard bounded DEDP. Our suggested hybrid method GA-SQP converges to achieve the best optimal solution in a confined environment in a limited number of simulations. The simulation results demonstrate applicability and adequacy of the given hybrid schemes over conventional methods.

Correlation Analysis of Synchronization Type and Degree in Respiratory Neural Network

Pre-Bötzinger complex (PBC) is a necessary condition for the generation of respiratory rhythm. Due to the existence of synaptic gaps, delay plays a key role in the synchronous operation of coupled neurons. In this study, the relationship between synchronization and correlation degree is established for the first time by using ISI bifurcation and correlation coefficient, and the relationship between synchronization and correlation degree is discussed under the conditions of no delay, symmetric delay, and asymmetric delay. The results show that the phase synchronization of two coupling PBCs is closely related to the weak correlation, that is, the weak phase synchronization may occur under the condition of incomplete synchronization. Moreover, the time delay and coupling strength are controlled in the modified PBC network model, which not only reveals the law of PBC firing transition but also reveals the complex synchronization behavior in the coupled chaotic neurons. Especially, when the two coupled neurons are nonidentical, the complete synchronization will disappear. These results fully reveal the dynamic behavior of the PBC neural system, which is helpful to explore the signal transmission and coding of PBC neurons and provide theoretical value for further understanding respiratory rhythm.