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Smart nonlinear circuits can be tamed to reproduce the main dynamical properties in neural activities and thus neural circuits are built to estimate the occurrence of multiple modes in electric activities. In the presence of electromagnetic radiation, the cardiac tissue, brain and neural circuits are influenced because field energy is injected and captured when induction field and current are generated in the media and system. In this paper, an isolated Chua circuit is exposed to external electromagnetic field and energy capturing is estimated for nonlinear analysis from physical viewpoint. Furthermore, two Chua circuits without direct variable coupling are exposed to the same electromagnetic field for energy capturing. Periodical and noise-like radiations are imposed on the Chua circuits which can capture the magnetic field energy via the induction coil. It is found that the two Chua circuits (periodical or chaotic) can reach phase synchronization and phase lock in the presence of periodical radiation. On the other hand, noise-like radiation can realize complete synchronization between two chaotic Chua circuits while phase lock occurs between two Chua circuits in periodical oscillation. It gives some important clues to control the collective behaviors of neural activities under external field. [ABSTRACT FROM AUTHOR]

The survival and occurrence of chaos are much dependent on the intrinsic nonlinearity and parameters region for deterministic nonlinear systems, which are often represented by ordinary differential equations and maps. When nonlinear circuits are mapped into dimensional dynamical systems for further nonlinear analysis, the physical parameters of electric components, e.g. capacitor, inductor, resistance, memristor, can also be replaced by dynamical parameters for possible adjustment. Slight change for some bifurcation parameters can induce distinct mode transition and dynamics change in the chaotic systems only when the parameter is adjustable and controllable. In this paper, a thermistor is included into the chaotic Chua circuit and the temperature effect is considered by investigating the mode transition in oscillation and the dependence of Hamilton energy on parameters setting in thermistor. Furthermore, the temperature of thermistor is adjusted for finding possible synchronization between two chaotic Chua circuits connected by a thermistor. When the coupling channel via thermistor connection is activated, two identical Chua circuits (periodical or chaotic oscillation) can reach complete synchronization. In particular, two periodical Chua circuits can be coupled to present chaotic synchronization by taming parameters in thermistor of coupling channel. However, phase synchronization is reached while complete synchronization becomes difficult when the coupling channel is activated to coupling a periodical Chua circuit and a chaotic Chua circuit. It can give guidance for further control of firing behaviors in neural circuits when the thermistor can capture the heat effectively. [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]

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]