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Spatial pattern formation and selection depend on the intrinsic self-organization and cooperation between nodes in spatiotemporal systems. Based on a memory neuron model, a regular network with electromagnetic induction is proposed to investigate the synchronization and pattern selection. In our model, the memristor is used to bridge the coupling between the magnetic flux and the membrane potential, and the induction current results from the time-varying electromagnetic field contributed by the exchange of ion currents and the distribution of charged ions. The statistical factor of synchronization predicts the transition of synchronization and pattern stability. The bifurcation analysis of the sampled time series for the membrane potential reveals the mode transition in electrical activity and pattern selection. A formation mechanism is outlined to account for the emergence of target waves. Although an external stimulus is imposed on each neuron uniformly, the diversity in the magnetic flux and the induction current leads to emergence of target waves in the studied network.

Autapse plays an important role in regulating the electric activity of neuron by feedbacking time-delayed current on the membrane of neuron. Autapses are considered in a local area of regular network of neurons to investigate the development of spatiotemporal pattern, and emergence of spiral wave is observed while it fails to grow up and occupy the network completely. It is found that spiral wave can be induced to occupy more area in the network under optimized noise on the network with periodical or no-flux boundary condition being used. The developed spiral wave with self-sustained property can regulate the collective behaviors of neurons as a pacemaker. To detect the collective behaviors, a statistical factor of synchronization is calculated to investigate the emergence of ordered state in the network. The network keeps ordered state when self-sustained spiral wave is formed under noise and autapse in local area of network, and it independent of the selection of periodical or no-flux boundary condition. The developed stable spiral wave could be helpful for memory due to the distinct self-sustained property.

Played as an important nonlinear electric device, memristor is often used to build a variety of nonlinear circuits, which can produce a variety of modes in oscillation. Due to the memory effect, the dynamics of nonlinear circuits involved with memristor can show distinct transition in oscillation between periodic and chaotic states when the initial values are changed. As a result, a generic initial-dependent dynamical system is built and its memory on initial setting is explained. The physical properties and potential mechanism for resistor-based voltage coupling, memristor coupling, capacitor-based and inductor-based field coupling are explained, respectively. In this review, scale transformation, application of memristor on neurodynamics, time delay, synchronization pattern, particularly, electromagnetic induction and radiation, neuron model setting under field effect, field coupling on signal propagation between nonlinear circuits and neurons are summarized for readers' extensive investigation. [ABSTRACT FROM AUTHOR]

The exchange of charged ions across membrane can generate fluctuation of membrane potential and also complex effect of electromagnetic induction. Diversity in excitability of neurons induces different modes selection and dynamical responses to external stimuli. Based on a neuron model with electromagnetic induction, which is described by magnetic flux and memristor, a two-layer network is proposed to discuss the pattern control and wave propagation in the network. In each layer, gap junction coupling is applied to connect the neurons, while field coupling is considered between two layers of the network. The field coupling is approached by using coupling of magnetic flux, which is associated with distribution of electromagnetic field. It is found that appropriate intensity of field coupling can enhance wave propagation from one layer to another one, and beautiful spatial patterns are formed. The developed target wave in the second layer shows some difference from target wave triggered in the first layer of the network when two layers are considered by different excitabilities. The potential mechanism could be pacemaker-like driving from the first layer will be encoded by the second layer. [ABSTRACT FROM AUTHOR]

In this paper, a new four-variable dynamical system is proposed to set chaotic circuit composed of memristor and Josephson junction, and the dependence of chaotic behaviors on nonlinearity is investigated. A magnetic flux-controlled memristor is used to couple with the RCL-shunted junction circuit, and the dynamical behaviors can be modulated by changing the coupling intensity between the memristor and the RCL-shunted junction. Bifurcation diagram and Lyapunov exponent are calculated to confirm the emergence of chaos in the improved dynamical system. The outputs and dynamical behaviors can be controlled by the initial setting and external stimulus as well. As a result, chaos can be suppressed and spiking occurs in the sampled outputs under negative feedback, while applying positive feedback type via memristor can be effective to trigger chaos. Furthermore, it is found that the number of multi-attractors in the Jerk circuit can be modulated when memristor coupling is applied on the circuit. These results indicate that memristor coupling can be effective to control chaotic circuits and it is also useful to reproduce dynamical behaviors for neuronal activities. [ABSTRACT FROM AUTHOR]

Complex electrical activities in neuron can induce time-varying electromagnetic field and the effect of various electromagnetic inductions should be considered in dealing with electrical activities of neuron. Based on an improved neuron model, the effect of electromagnetic induction is described by using magnetic flux, and the modulation of magnetic flux on membrane potential is realized by using memristor coupling. Furthermore, additive phase noise is imposed on the neuron to detect the dynamical response of neuron and phase transition in modes. The dynamical properties of electrical activities are detected and discussed, and double coherence resonance behavior is observed, respectively. Furthermore, multiple modes of electrical activities can be observed in the sampled time series for membrane potential of the neuron model. [ABSTRACT FROM AUTHOR]

Based on an improved neuronal model, in which the effect of magnetic flux is considered during the fluctuation and change of ion concentration in cells, the transition of synchronization is investigated by imposing external electromagnetic radiation on the coupled neurons, and networks, respectively. It is found that the synchronization degree depends on the coupling intensity and the intensity of external electromagnetic radiation. Indeed, appropriate intensity of electromagnetic radiation could be effective to realize intermittent synchronization, while stronger intensity of electromagnetic radiation can induce disorder of coupled neurons and network. Neurons show rhythm synchronization in the electrical activities by increasing the coupling intensity under electromagnetic radiation, and spatial patterns can be formed in the network under smaller factor of synchronization. [ABSTRACT FROM AUTHOR]

Signal propagation can be blocked when the axon is injured or ion channels are blocked by certain drug, and thus signal communication between neurons can be interrupted. It is found that defects could be induced in the injured area of the axon, and the local heterogeneity can emit continuous pulses or wave fronts. In this paper, a weak electric field is imposed on the neuron to suppress the blocking of the defects on signal propagation. It is found that appropriate electric field can help signal propagate along the axon even the electric field is imposed on a local area. Its potential mechanism could be that the local electric field can suppress the wave emitting from the defects and thus the injured area can be bridged to transmit the blocked signals by adding gradient forcing along the axon. [ABSTRACT FROM AUTHOR]

Appropriate noise can enhance the regularity in electrical activity of neuron, and stochastic resonance emerges when periodic forcing is imposed on the neuron and/or neuronal network. In this paper, periodic forcing is imposed on some neurons of a two-dimensional square lattice with nearest-neighbor connection (the boundary of one side in the network of neurons), which the local kinetics of node is described by Hindmarsh-Rose neuron, while noise is imposed on another side of the two-dimensional lattice. Indeed, spiral waves can be developed in the side of the network driven by appropriate noise intensity while the another side is occupied by plane wave. A statistical factor of synchronization is defined to discern the occurrence of regularity induced by local noise and local pacing. The emitted plane wave from one side of network can be suppressed by noise and disordered state emerges with stronger noise being used on all nodes of the network, furthermore, spiral wave is induced in the network under appropriate noise intensity. The network shows spatial regularity when spiral wave is developed and it is interesting to find spiral wave can coexist with plane wave in the network. Stochastic resonance-like behavior could be observed in the two-dimensional lattice composed of neurons even if noise and periodic forcing are imposed on different areas of the network. The occurrence of spatial regularity under coherence could rely on the competition between noise driving-induced segments and wave fronts induced by periodic forcing. [ABSTRACT FROM AUTHOR]

Spatiotemporal systems can emerge some regular spatial patterns due to self organization or under external periodical pacing while external attack or intrinsic collapse can destroy the regularity in the spatial system. For an example, the electrical activities of neurons in nervous system show regular spatial distribution under appropriate coupling and connection. It is believed that distinct regularity could be induced in the media by appropriate forcing or feedback, while a diffusive collapse induced by continuous destruction can cause breakdown of the media. In this paper, the collapse of ordered spatial distribution is investigated in a regular network of neurons (Morris–Lecar, Hindmarsh–Rose) in two-dimensional array. A stable target wave is developed regular spatial distribution emerges by imposing appropriate external forcing with diversity, or generating heterogeneity (parameter diversity in space). The diffusive invasion could be produced by continuous parameter collapse or switch in local area, e.g, the diffusive poisoning in ion channels of potassium in Morris–Lecar neurons causes breakdown in conductance of channels. It is found that target wave-dominated regularity can be suppressed when the collapsed area is diffused in random. Statistical correlation functions for sampled nodes (neurons) are defined to detect the collapse of ordered state by series analysis. [ABSTRACT FROM AUTHOR]

A temperature-dependent nonlinear circuit can be mapped into an equivalent thermosensitive neuron model and then the main dynamical properties of neural activities can be reproduced. A thermistor is connected to different branch circuits of the FHN (FitzHugh–Nagumo) neural circuit, and different thermosensitive neuron models are obtained by applying scale transformation on the parameters and physical variables. The dynamics of the thermosensitive neurons is dependent on the temperature greatly, and synchronization stability between these neurons is investigated by selecting different kinds coupling channels. The reliability of this coupling scheme is mainly controlled by the physical properties of the electronic components in the coupling channels. A capacitor (and induction coil) can be used to connect nonlinear circuits and field coupling is activated to pump field energy for realizing synchronization. This kind of field coupling shows some advantage than the known voltage coupling via resistor connection because of no consumption of Joule heat and the coupling channel is adjustable. The results confirmed that two identical temperature-sensitive neurons can be coupled to reach complete synchronization by regulating the physical parameters in the coupling channel, and energy pumping along the coupling channel is decreased to zero under complete synchronization. For two thermosensitive neurons with parameter mismatch and diversity in temperature, synchronization approach becomes difficult and the energy pumping in the coupling channel is continued under phase lock. Its biophysical significance is that diversity in excitability and difference in channels makes thermosensitive neurons become much different, and the occurrence of bursting synchronization and seizure can be prevented completely. [ABSTRACT FROM AUTHOR]

Phototube can capture and transmit external illumination with high frequency into photocurrent in the nonlinear circuit, which can be tamed to produce the main dynamical properties of biological neurons. In fact, the involvement of functional electronic components can enhance the biophysical function of artificial neural circuits. In this paper, a photocell is connected to FitzHugh-Nagumo neural circuits, which can be excited by the photocurrent generated from the photocell. Furthermore, a memristor is proposed to couple two light-dependent neural circuits and the synchronization stability is investigated on the coupled dynamical systems by using standard scale transformation on the physical variables and parameters. It is found that phase synchronization and complete synchronization can be obtained by regulating the coupling channel connected by the memristor. The propagation and pumping of field energy are also calculated to predict the occurrence of synchronization. [ABSTRACT FROM AUTHOR]