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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]

Nervous system has distinct anisotropy and some intrinsic biophysical properties enable neurons present various firing modes in neural activities. In presence of realistic electromagnetic fields, non-uniform radiation activates these neurons with energy diversity. By using a feasible model, energy function is obtained to predict the growth of synaptic connections of these neurons. Distribution of average value of the Hamilton energy function vs. intensity of noisy disturbance can predict the occurrence of coherence resonance, which the neural activities show high regularity by applying noisy disturbance with moderate intensity. From physical viewpoint, the average energy value has similar role average power for the neuron. Non-uniform spatial disturbance is applied and energy is injected into the neural network, statistical synchronization factor is calculated to predict the network synchronization stability and wave propagation. The intensity for field coupling is adaptively controlled by energy diversity between adjacent neurons. Local energy balance will terminate further growth of the coupling intensity; otherwise, heterogeneity is formed in the network due to energy diversity. Furthermore, memristive channel current is introduced into the neuron model for perceiving the effect of electromagnetic induction and radiation, and a memristive neuron is obtained. The circuit implement of memristive circuit depends on the connection to a magnetic flux-controlled memristor into the mentioned neural circuit in an additive branch circuit. The connection and activation of this memristive neural network are controlled under external spatial electromagnetic radiation by capturing enough field energy. Continuous energy collection and exchange generate energy diversity and synaptic connection is created to regulate the synchronous firing patterns and energy balance. • A feasible memristive neuron is proposed and its physical property is clarified. • Average Hamilton energy is effective to predict coherence resonance under noisy disturbance. • Non-uniform radiation is applied on the neural network with adaptive coupling. • Energy level controls the growth of synaptic connections. [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]

Pattern estimation and selection in media can give important clues to understand the collective response to external stimulus by detecting the observable variables. Both reaction-diffusion systems (RDs) and neuronal networks can be treated as multi-agent systems from molecular level, intrinsic cooperation, competition. An external stimulus or attack can cause collapse of spatial order and distribution, while appropriate noise can enhance the consensus in the spatiotemporal systems. Pattern formation and synchronization stability can bridge isolated oscillators and the network by coupling these nodes with appropriate connection types. As a result, the dynamical behaviors can be detected and discussed by developing different spatial patterns and realizing network synchronization. Indeed, the collective response of network and multi-agent system depends on the local kinetics of nodes and cells. It is better to know the standard bifurcation analysis and stability control schemes before dealing with network problems. In this review, dynamics discussion and synchronization control on low-dimensional systems, pattern formation and synchronization stability on network, wave stability in RDs and neuronal network are summarized. Finally, possible guidance is presented when some physical effects such as polarization field and electromagnetic induction are considered. [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]

Abstract Local periodic stimulus can trigger stable pulse and target wave in the excitable media, the potential mechanism is that each cell is activated by continuous driving to keep pace with the external forcing. Indeed, local diversity in excitability and heterogeneity are induced when external forcing with diversity is applied on the media. When target wave is formed and propagated, the media will be modulated, e.g. it can emit electric signal from sinoatrial node and develops target wave in the cardiac tissue, and then the heartbeat is controlled completely. In fact, the distribution of electromagnetic field in the media is changed when external electric stimulus is applied on the media; therefore, the effect of electromagnetic induction becomes important during the information encoding and signal propagation. In this paper, the Morris–Lecar model is used to describe the local kinetic of the media and an induction current is considered thus the effect of electromagnetic induction can be described. Then the artificial heterogeneity is triggered to investigate the formation and development of target waves in the excitable media with electromagnetic induction and even radiation, which is described by using Gaussian white noise. Diversity in excitability and conductance of ion channels is considered, respectively, thus different kinds of artificial heterogeneity are developed to find the stability of target waves. It is found that the target wave encounters breakup with increasing of the intensity of electromagnetic radiation. Highlights • Biological neuron model is improved to consider the effect of electromagnetic induction. • Heterogeneity formation is explained on conductance and excitability diversity. • Electromagnetic radiation can suppress propagation of target wave. • Breakup of target wave can be induced by electromagnetic radiation. [ABSTRACT FROM AUTHOR]