Emergence of spiral wave induced by defects block

The development of spiral wave in the regular network of Hindmarsh–Rose neurons with nearest-neighbor connection is investigated under no-flux and/or periodical boundary condition, respectively. At first, specific initial values are selected to detect the formation of spiral wave, it is found that the developed state is controlled by the bifurcation ss, which controls the electric activity of neuron from spiking to burst behavior, and different developed states are observed. Furthermore, the formation of ordered wave induced by the defect block in the network of neurons is also investigated. In the numerical studies, the first step is to generate target-like wave by imposing a discrepant forcing current (not periodical signal) on a local region, the second step is to produce an artificial defect by setting the variables in a local area to zero. The supposed defect is used to block the propagation of target wave in the network, and the condition for spiral wave emergence is investigated in a numerical way. It indicates that the existence of defect in the media accounts for the emergence of spiral wave though most of the previous works used to simulate the development of spiral wave by using specific initial values. A statistical factor of synchronization in the two-dimensional space is defined to detect the appearance and robustness of spiral wave in the network of neurons. It is confirmed that the contour profile of the developed pattern is dependent on the intensity of coupling and defects block.

► Mechanism of spiral wave formation in excitable media is discussed.
► How to design target wave and defect are suggested in simple way.
► The effect of periodical and/no-flux boundary condition is compared.
► Factor of synchronization is helpful to detect the survival of spiral wave.