Synchronization behaviors of coupled neurons under electromagnetic radiation

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.

TRANSITION OF SPIRAL WAVE IN A MODEL OF TWO-DIMENSIONAL ARRAYS OF HINDMARSH–ROSE NEURONS

In this paper, the condition of completely nearest-neighbor couplings is introduced into the coupled Hindmarsh–Rose neurons in two-dimensional arrays. It is found that the stable rotating spiral wave can be developed and the transition of spiral wave in the coupled Hindmarsh–Rose neurons are investigated. The factor of synchronization is defined to investigate the development and instability of the spiral wave. Furthermore, the external injected current, coupling coefficients and other decisive bifurcation parameter r and χ, are endowed with different values to study the transition of spiral wave by analyzing the factor of synchronization and the snapshots of the activator. It is found that the critical sudden change points in the curve for factor of synchronization often indicates sudden transition of spiral wave, the instability or death of the spiral wave. The snapshots are also plotted to confirm the results from the curve of the factor of synchronization. Finally, the noise-induced instability and chaotic logistic map-induced instability of spiral wave are investigated and discussed.

COLLECTIVE BEHAVIORS OF SPIRAL WAVES IN THE NETWORKS OF HODGKIN-HUXLEY NEURONS IN PRESENCE OF CHANNEL NOISE

Collective behaviors of spiral waves in the networks of Hodgkin-Huxley neuron are investigated. A stable rotating spiral wave can be developed to occupy the quiescent areas in networks of neurons by selecting appropriate initial values for the variables in the networks of neurons. In our numerical studies, most neurons are quiescent and finite (few) numbers of neurons are selected with different values to form a spiral seed. In this way, neurons communicating are carried by propagating spiral wave to break through the quiescent domains (areas) in networks of neurons. The effect of membrane temperature on the formation of spiral wave is investigated by selecting different fixed membrane temperatures in the networks, and it is found that a spiral wave cannot be developed if the membrane temperature is close to a certain threshold. A quantitative factor of synchronization is defined to measure the statistical properties and collective behaviors of the spiral wave. And a distinct phase transition, which indicates the critical condition for spiral survival, is observed in the sudden changing point of the factors of synchronization curve vs. certain bifurcation parameter. Internal noise is introduced into ion channels (channel noise) with the Langevin method. It is found that a stable rotating spiral wave is developed and the spiral wave is robust to weak channel noise (the membrane patch is not small). The spiral wave can not grow up and the stable rotating spiral wave encounters instability in presence of strong channel noise. Coherence resonance-like behavior is observed in calculating the factors of synchronization in presence of channel noise.