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•A neuron membrane with two capacitive variables is presented.•Light-sensitive ion channel is designed to enhance light sensitivity property of functional membrane.•Energy function is defined to discern its dependence on firing modes.•An adaptive law controls the growth of capacitive parameters under energy flow.

Both capacitor and charge-controlled memristor (CCM) can regulate the inner energy levels during the release and accumulation of charges in these electronic components. Combination of inductive and capacitive components is crucial to build an oscillatory circuit, and incorporation of a nonlinear resistor is helpful to support nonlinear oscillation under continuous energy exchange between magnetic field and electric field. Relation between physical variables in neural circuits can be described by some equivalent nonlinear oscillators by applying scale transformation on the variables and parameters for the neural circuit, and the energy function becomes available from theoretical approach. In this work, a simple neural circuit coupled with a CCM is designed to obtain a memristive neuron model, and then linear transformation is applied to the sampled variables involved with time scale for time step, a new memristive map is obtained to discuss its energy characteristic and self-controllability under energy flow. The result provides guidance to measure the reliability of maps, and the new derived maps with reliable physical evidences can be further used in digital signal processing. • Memristive neuron and memristive map are presented. • Linear transformation from oscillator to equivalent map is presented. • Energy function for a memristive map is defined. • Adaptive law is proposed to activate mode transition and energy shift in the map neuron. [ABSTRACT FROM AUTHOR]

Synapse is an important bridge for receiving and encoding signals, and the description for synapse current is critical for further signal processing. This paper investigates the dynamical characteristic in isolated neuron and chain neuronal networks with memristive autapse or synapses, respectively. Autapse plays important role in modulating the electrical activities, and thus the information encoding is enhanced. Within the improved neuron model, memristor is used to map the modulation of synapse current. Within an isolated new neuron model with memory, the modes in electrical activities can be controlled by the synapse current completely. Bifurcation analysis is carried out and mode transition is discussed. Furthermore, the modulation of synapse current on chain network is investigated, and the dependence of wave propagation on intensity of synapse is discussed. The diversity in synapse current can suppress the synchronization approach on the network. [ABSTRACT FROM AUTHOR]

Autapse connected to the neuron can change the electric activity of neuron. The effect of autapse on neuronal activity is often described by adding an additive forcing current along a close loop, which is described by a time-delayed feedback on the membrane potential. Neuron often responds to electric autapse forcing sensitively and quickly, while the chemical autapse changes the electric activity of neuron slowly. By applying external forcing, a shift transition of electric activity can be more easily induced by the electric autapse than the chemical autapse. Our results confirm that chemical autapse can enhance and/or suppress the transition of electric activity with excitable or inhibitory type driven by electric autapse, vice versa. It indicates that an appropriate switch-off-on for autapse can make the neuron give different types of response to external forcing. Particularly, cooperation and competition between chemical and electric autapse help neuron response to external forcing in the most reliable way.

Autapse is a type of synapse that connects axon and dendrites of the same neuron, and the effect is often detected by close-loop feedback in axonal action potentials to the owned dendritic tree. An artificial autapse was introduced into the Hindmarsh-Rose neuron model, and a regular network was designed to detect the regular pattern formation induced by autapse. It was found that target wave emerged in the network even when only a single autapse was considered. By increasing the (autapse density) number of neurons with autapse, for example, a regular area (2×2, 3×3, 4×4, 5×5 neurons) under autapse induced target wave by selecting the feedback gain and time-delay in autapse. Spiral waves were also observed under optimized feedback gain and time delay in autapses because of coherence-like resonance in the network induced by some electric autapses connected to some neurons. This confirmed that the electric autapse has a critical role in exciting and regulating the collective behaviors of neurons by generating stable regular waves (target waves, spiral waves) in the network. The wave length of the induced travelling wave (target wave, spiral wave), because of local effect of autapse, was also calculated to understand the waveprofile in the network of neurons.

The effect of autapse on adjusting the membrane of potentials of neuron is described by imposing a time-delayed feedback on the membrane of neuron in a close loop type, and the Hindmarsh-Rose (HR) neuron under autapse is investigated. Firstly, the electric activity of single HR neuron under electric autapse and chemical autapse is investigated. It is found that quiescent neuron is activated due to appropriate time delay and feedback gain in the autapse, and the autapse plays an important role in waking up neuron. The parameter region for periodic, chaotic activity of neuron under autapse is calculated in a numerical way, and transition from spiking to bursting is observed by increasing the feedback gain and time delay carefully. Furthermore, the collective electric activities of neurons in a ring network is investigated and abundant electric activities are observed due to the competition between the autapse and the time-delayed coupling between adjacent neurons in the network, and time delay in coupling between neurons also plays an important role in enhancing synchronization in the network.

The electric activities of neurons could be changed when ion channel block occurs in the neurons. External forcing currents with diversity are imposed on the regular network of Hodgkin-Huxley (HH) neuron, and target waves are induced to occupy the network. The forcing current I1is imposed on neurons in a local region with m0×m0nodes in the network, neurons in other nodes are imposed with another forcing current I2. Target wave could be developed to occupy the network when the gradient forcing current (I1–I2) exceeds certain threshold, and the formation of target wave is independent of the selection of boundary condition. It is also found that the developed target wave can decrease the negative effect of ion channel block and suppress the spiral wave, and thus channel noise is also considered. The potential mechanism of formation of target wave could be that the gradient forcing current (I1–I2) generates quasi-periodical signal in local area, and the propagation of quasi-periodical signal induces target-like wave due to mutual coupling among neurons in the network.

• Three kinds of functional neurons are presented. • Magnetic field coupling is the main bridge for different functional neurons. • Electric synapse coupling and electric field coupling corrupt synchronization stability between different neurons. Specific biophysical neurons are presented to detect different stimuli, and these external exciting signals are encoded to trigger appropriate firing modes and action potentials for signal propagation between neurons in the network. A thermosensitive neuron can estimate the effect of temperature changes on the excitability and firing modes in nervous system, a photocurrent-dependent neuron can be sensitive to the changes of external illumination or light, and an auditory neuron can perceive acoustic wave when the vibration energy is absorbed and converted into field energy in the loop of neural circuits. From biophysical viewpoint, some specific electric components such as thermistor, phototube, and piezoelectric ceramics can be incorporated into neural circuits for activating specific functions, and thus the external stimuli such as heat, light and vibration can be detected because these energy injections can be converted to intrinsic field energy in the neural circuits. In this paper, three kinds of different neural circuits are coupled in a close loop, energy pumping and the stability of phase synchronization are investigated by regulating the properties of coupling channels, furthermore, the noise effect is also estimated. When induction coil is used to couple the neural circuits, phase stability is controlled under magnetic field coupling, and the activation of noise can change the stability of phase synchronization. The intrinsic field energy in the light-dependent neuron is increased with the increase of coupling intensity when voltage coupling via resistor and magnetic field coupling via induction coil are switched on. In case of electric field coupling via capacitor, the energy in the light-dependent neural circuit keeps oscillatory with small amplitude. These results indicate that magnetic field can be the most suitable way for realizing synchronous information encoding between different functional neurons than the electric synapse coupling because continuous pumping of ions can induce magnetic field in the cell, and all the neurons are controlled completely by effective pumping in field energy. [ABSTRACT FROM AUTHOR]

Both electrical and chemical synapses play important role in receiving and propagating signals between biological neurons. The activation of electrical synapse coupling is generated via gap junction connection while chemical synapse coupling depends on the release of neurotransmitter for triggering stable propagation of ions. In a practical way, voltage coupling via resistor connection between artificial neural circuits is often used to describe the gap junction coupling via electrical synapse between neurons. Magnetic field coupling via induction coil between neural circuits can be effective to estimate the chemical synapse coupling when ions are propagated and released in the cell. In this paper, the physical properties of magnetic field coupling between neural circuits are discussed. For simplicity, two Hindmarsh–Rose neurons are connected to trigger magnetic field coupling and the coupling channel is tamed to detect possible occurrence of synchronization. Two neurons are stimulated with different stimuli, and it is confirmed that the synchronous firing mode is decided by the neuron with higher forcing amplitude. Furthermore, the collective behaviors of HR neuron in the small-world network and scale free network are investigated by changing the coupling intensity and diversity in external stimulus, respectively. Statistical synchronization factor is calculated to estimate the dependence of synchronization on coupling gain and the number of bursting neurons in the network. In case of small-world connection, synchronization approach becomes difficult. However, complete synchronization can be stabilized on the scale free network under magnetic field coupling. [ABSTRACT FROM AUTHOR]

To assess the feasibility of dose escalation guided by 18F-deoxyglucose positron emission tomography/computer tomography (18F-FDG PET/CT) for esophageal cancer (EC).

The modes of electric activities in neurons and wave propagation between neurons can be changed by using appropriate external forcing or coupling type. Based on the PSpice tool, the coupling synchronization between three Hindmarsh-Rose neurons is investigated. The neuronal circuit is also designed, and the Schmitt trigger circuit is used as peak detector by transmitting the analog signal into digital signal; thus, the rhythm of electric activities of neurons can be analyzed. By selecting different initial states (spiking or bursting), different synchronization states are found. In the case of spiking state, appropriate coupling intensity is effective in realizing rhythm synchronization and then homogenous state is observed by further increasing the coupling intensity. In the case of bursting state, rhythm synchronization is enhanced under appropriate coupling intensity while desynchronization occurs by further increasing the coupling intensity.

Based on the Fitzhugh–Nagumo neuron model, the effect of electromagnetic induction is considered and external electromagnetic radiation is imposed to detect the mode transition of electrical activities in a myocardial cell. Appropriate dynamical and functional responses can be observed in the sampled series for membrane potentials by setting different feedback modulation on the membrane potential in presence of electromagnetic radiation. The electromagnetic radiation is described by a periodical forcing on the magnetic flux, and it is found that the response frequency can keep pace with the frequency of external forcing. However, mismatch of frequency occurs by further increasing the frequency of external forcing, it could account for the information encoding of neuron. The dynamical response could be associated with the magnetization and polarization of the media, thus the outputs of membrane potential can become quiescent and/or bursting as well. [ABSTRACT FROM AUTHOR]

Autapse is an unusual type of synapse generated by a neuron on itself. The effect of autapse connected to a neuron is often described by using a self-feedback forcing current in a close loop, and the electric activities of neuron can be regulated by the autapse greatly. Generally, positive feedback in the autapse can excite the quiescent neuron while negative feedback often calms down the excitable neuron. In this paper, the Hindmarsh–Rose neuron model is used to define the local kinetics of each node in the neuronal network, and the distribution of autapses in the network is considered to investigate the emergence of emitting wave induced by autapse (in electrical type) with negative feedback. In the case of ring network, it is found that pulse can be blocked by the neurons with negative feedback in autapse, and the pulse also can keep alive in the ring network stably under appropriate coupling intensity. Furthermore, target wave can be induced in the two-dimensional square array, and the nodes adjusted by negative electrical feedback type in autapses can emit target-like waves to regulate the collective behaviors of neurons, this is a new type of wave formation results from diffraction. It concludes that local distribution of autapse with negative feedback type can generate ‘defects’ in the network, the diversity in excitability accounts for the emergence of emitting wave from these defects. Finally, the functional switch between negative and positive feedback in autapse is discussed, it is claimed that positive feedback autapse plays an important role in cheering up quiescent neurons, while the negative feedback in electric autapse can contribute to slow down the excitable neurons. [ABSTRACT FROM AUTHOR]

Some nonlinear circuits can present similar dynamical properties in the outputs as biological neurons by taming the external stimulus and bifurcation parameter, and they can be used for further investigation on neural activities. In this work, a photoelectric converter such as phototube is incorporated into the Fitzhugh-Nagumo neural circuit and a light-sensitive neuron is obtained to describe the nonlinear response in visual neuron. Furthermore, an additive induction coil is also connected to the phototube in this branch circuit of this neural circuit for detecting the disturbance from external magnetic field, and this functional neuron can perceive external illumination and changes of external magnetic field synchronously. Scale transformation is applied for the circuit equation and equivalent photoelectric neuron model is obtained. The intrinsic field energy of the neural circuit is described by equivalent Hamilton energy and the dependence firing modes on energy is clarified. When neurons are clustered closely, energy diversity can trigger field coupling and the synaptic connection will be regulated in the coupling intensity adaptively. An artificial hybrid is developed by combining capacitor and inductor in the coupling channel, and synchronization approach and energy balance is controlled completely. These results provide potential explanation for knowing the growth mechanism for synapse connection and external energy injection can be effective to control the collective behaviors of neurons. • A functional neural circuit is designed to detect external illumination and magnetic field. • Hamilton energy for biological neuron is obtained. • Stochastic resonance is induced in the biophysical neuron under noisy magnetic field. • Hybrid synapse is controllable under energy flow. • Biophysical mechanism for synapse controllability is explained. [ABSTRACT FROM AUTHOR]

Abnormal electrical activities in neuronal system could be associated with some neuronal diseases. Indeed, external forcing can cause breakdown even collapse in nervous system under appropriate condition. The excitable media sometimes could be described by neuronal network with different topologies. The collective behaviors of neurons can show complex spatiotemporal dynamical properties and spatial distribution for electrical activities due to self-organization even from the regulating from central nervous system. Defects in the nervous system can emit continuous waves or pulses, and pacemaker-like source is generated to perturb the normal signal propagation in nervous system. How these defects are developed? In this paper, a network of neurons is designed in two-dimensional square array with nearest-neighbor connection type; the formation mechanism of defects is investigated by detecting the wave propagation induced by external forcing. It is found that defects could be induced under external periodical forcing under the boundary, and then the wave emitted from the defects can keep balance with the waves excited from external forcing. [ABSTRACT FROM AUTHOR]

Abstract: The chaotic circuit of resistive–capacitive–inductive-shunted Josephson junction is used to simulate behavior of Hindmarsh–Rose neuronal discharges. Based on tracking control theory, the controller contains two gain coefficients was constructed to control the chaotic system of Josephson junction to synchronize the chaotic Hindmarsh–Rose system, and the single controller was approached analytically. The results confirmed that the controller with appropriate gain coefficients was effective to reach complete synchronization (the amplitudes and rhythms of two systems are identical), phase synchronization (rhythms of two systems are identical) of Josephson junction and Hindmarsh–Rose neurons, respectively. The power consumption is estimated in a feasible way. As a result, the electric activities of Hindmarsh–Rose neurons could be simulated by using Josephson junction model completely. [Copyright &y& Elsevier]

• Thermistor can control the dynamics in nonlinear circuit and temperature effect is estimated. • Time-varying and adjustable coupling can be triggered to control network synchronization. • Target wave can be induced and propagated in network due to diversity in temperature. Pattern formation and synchronization stability in the network are dependent on the local kinetics, connection type, and property of coupling channel. The coupling channels is often controlled to reach synchronization and pattern selection. From dynamical viewpoint, all the bifurcation parameters and coupling channels can be adjusted to get desired patterns and behaviors. However, the physical parameters for most of the electronic components are fixed even some of them can be adjusted in slight range. Thermistor is a kind of nonlinear electronic components, and its resistance is dependent on the temperature completely. It can be used to detect the fluctuation of environment temperature by building nonlinear circuits composed of thermistors. The coupling channel can be adjusted by the temperature when the thermistors are used to couple two or more nonlinear circuits. In this paper, the thermistors are used to couple Chua circuits in a square array with regular connection between adjacent nodes in the network. Gradient distribution of temperature on the network can induce diversity in the coupling intensity in the network because the channel resistances of the coupling thermistors are influenced by the heterogeneous distribution of temperature. In fact, the nodes close to the heat source have higher temperature and they are coupled with stronger intensity because of lower resistances for the coupling thermistors. Perfect target waves can be induced and propagated in the network by taming the temperature for coupling channels. Furthermore, statistical synchronization factor is calculated to estimate the synchronization stability and wave propagation in the network. These results suggested that physical components with adjustable parameters can be used in practical control of nonlinear systems. [ABSTRACT FROM AUTHOR]