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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]

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]