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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]

• 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]

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]

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]

• 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]