The development of the double-spiral wave is plotted with diversity in coupling intensity being considered.

<p>The coupling intensity for nodes outside the inboard spiral wave is decreased to while the coupling intensity for the nodes in the inserted square() is kept as . (a), (b), (c), (d), no external forcing current is imposed on the network().</p

The development of , vs. collision times when 8-arm spiral wave is induced in the center of the network.

<p>It begins from initial time , initial space bridges 30 nodes in the network along polar axis. The coupling intensity for nodes () is selected as , the other nodes are coupled with intensity , no external forcing current is imposed on the network().</p

The diagrammatic sketch (a) for spatial forcing currents on controlled nodes in the network.

<p>Spatial forcing current at (and at ) are imposed on the nodes(solid black spots) in the network. (a1) for 2-arm spiral wave, (a2) for 3-arm spiral wave, (a4) for 4-arm spiral wave, (a5) for 8-arm spiral wave. The developed pattern for <i>t</i> = 200 ms(b)(enhanced online). The snapshots(two-arm, three arm, four-arm, five-arm, eight-arm spiral waves) illustrate the distribution for membrane potentials of neurons in gray scale, the coupling intensity , the forcing currents on the rest nodes are .</p

The development of ,vs. collision times (a) when 2-arm spiral wave is induced in the center of the network.

<p>(b) The developed 2-arm spiral wave at . It begins from initial time , initial space bridges 27 nodes in the network along polar axis. The coupling intensity for all nodes is selected as , external forcing current on all nodes is selected as .</p

The development of , vs. collision times when 8-arm spiral wave is induced in the center of the network.

<p>It begins from initial time , initial space bridges 30 nodes in the network along polar axis. The coupling intensity for all nodes is selected as , no external forcing current is imposed on the network().</p

The development of , vs. collision times (a), the developed 2-arm spiral wave at .

<p>It begins from initial time , initial time , initial space bridges 40 nodes in the network along polar axis. The coupling intensity for nodes () is selected as , the other nodes are coupled with intensity , external forcing current on all nodes is selected as .</p

The diagrammatic sketch (a) for spatial forcing currents on the network.

<p>Spatial forcing currents are imposed on the nodes(two solid black spots and one of the circles) in the network, the developed pattern for <i>t</i> = 200 ms. The snapshot(b) illustrates the distribution for membrane potentials of neurons in gray scale, the coupling intensity , the forcing currents on the rest nodes are .</p

Multiarmed spiral waves with different arm numbers are developed in the network with certain transient period.

<p>For(a) 2-arm spiral wave at , for (b)3-arm spiral wave , for (c)4-arm spiral wave at , for (d)8-arm spiral wave at , no external forcing current is imposed on the network. The nodes close to the tips of inboard spiral waves are coupled with intensity , other nodes are coupled with intensity (similar to the illustration in Fig. 7).</p

Time series of membrane potential in N1 and N2 for different parameter values.

<p>The values of parameters , and are same as in Fig. 2. (a)(b) = 0.3,  = 0.9; (c)(d) = 0.5,  = 0.9. Note that the time scales are much longer than that in Fig. 2.</p

The diagrammatic sketch for the coordinate for the double-spiral wave in the network.

<p>In the case of polar coordinate, the connection line for point marks the polar axis, the point is regarded as the center for the tips of the double-spiral wave, respectively. Where represents the intersection point for the wavefronts of the double-spirals, and denotes the point of tangency on the wavefront of the outboard spiral wave and the corresponding tangent line is perpendicular to the polar axis.</p