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A variety of electric components can be used to bridge connection to the nonlinear circuits, and continuous pumping and consumption of energy are critical for voltage balance between the output end. The realization and stability of synchronization are mainly dependent on the physical properties of coupling channel, which can be built by using different electric components such as resistor, capacitor, induction coil and even memristor. In this paper, a memristive nonlinear circuit developed from Chua circuit is presented for investigation of synchronization, and capacitor, induction coil are jointed with resistor for building artificial synapse which connects one output of two identical memristive circuits. The capacitance and inductance of the coupling channel are carefully adjusted with slight step increase to estimate the threshold of coupling intensity supporting complete synchronization. As a result, the saturation gain method applied to realize the synchronization between chaotic circuits and physical mechanism is presented. [ABSTRACT FROM AUTHOR]

Reliable neural circuits provide feasible ways to estimate the information encoding and signal exchange between neurons so that more physical effects can be considered and explained. Electrical synapse benefits signal propagation and neurons can give rapid response selection under an external stimulus. Chemical synapse plays a standing biological function by the continuous release of neurotransmitter. Gap junction coupling can estimate the effect of electrical synapse coupling as resistor-based voltage coupling while chemical synapse coupling shows a complex form in synapse currents. In this paper, two FitzHugh–Nagumo neuron circuits are connected by resistor and induction coil, and thus field coupling is activated to realize synchronization. It gives possible guidance to explain the synapse function from physical view. These circuit equations are obtained and scale transformation is applied to get the dimensionless dynamical systems. Furthermore, the same scheme is used to discuss synchronization realization between Hindmarsh–Rose neuron models. It is found that synchronization can be suppressed when the coupling resistor is in series with the induction coil in which only one coupling channel is open. However, complete synchronization can be enhanced when the coupling resistor is paralleled with the induction coil because two coupling channels are activated simultaneously. As a result, appropriate adjustment and selection for the coupling electric devices can induce transition from synchronization to desynchronization between neural circuits, which indicates the self-adaption of synapse when two types of synapse are activated together. [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]

Based on a class of chaotic system composed of hidden attractors, in which the equilibrium points are described by a circular function, complete synchronization between two identical systems, pattern formation and synchronization of network is investigated, respectively. A statistical factor of synchronization is defined and calculated by using the mean field theory, the dependence of synchronization on bifurcation parameters discussed in numerical way. By setting a chain network, which local kinetic is described by hidden attractors, synchronization approach is investigated. It is found that the synchronization and pattern formation are dependent on the coupling intensity and also the selection of coupling variables. In the end, open problems are proposed for readers' extensive guidance and investigation. [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]

The Hodgkin-Huxley neuron model is used to describe the local dynamics of nodes in a two-dimensional regular network with nearest-neighbor connections. Multi-armed spiral waves emerge when a group of spiral waves rotate the same core synchronously. Here we have numerically investigated how multi-armed spiral waves are formed in such a system. Under the appropriate conditions, multi-armed spiral waves were able to develop as a result of adjusting the conductance of ion channels of particular neurons in the network. In a realistic neuron model, it can be practiced by blocking potassium of ion channels embedded in the membrane of neurons. For example, decreasing the potassium channel conductance in some neurons with a certain transient period can lead to the development of a group of double spirals in a localized area of the network. Furthermore, decreasing the excitability and the external forcing current to zero led to the growth of these double spirals and the formation of a stable multi-armed spiral wave that occupied the network under inhomogeneity. [ABSTRACT FROM AUTHOR]