Skip to main content
Figure 10 | The Journal of Mathematical Neuroscience

Figure 10

From: A phenomenological model of seizure initiation suggests network structure may explain seizure frequency in idiopathic generalised epilepsy

Figure 10

Escape times for networks of different sizes. Schematic illustration of how escape times scale with the size (number of nodes) in the network depending on the nature of the FTC when there are strong connections (large β). The diagonal black line represents balanced networks (those with u = 0). The horizontal lines represent networks of different sizes having the same FTC, coloured according to the number of nodes in the FTC, as specified in the legend. Dots indicate actual graphs and lines are used to convey visually the link between graphs of different size that have similar properties. For the class of balanced networks (u = 0) which includes all fully connected and symmetric networks among others, the escape time scales exponentially with the number of nodes in the network. This class of networks also has the largest escape times among networks of a given size. The horizontal lines represent networks of a given FTC, coloured according to the number of nodes in the FTC, n. As the network grows in size, provided the FTC is unchanged and the connections are strong, the escape time will remain practically unchanged, leading to the horizontal lines depicted here. For each of n = 1 and n = 2, there is only one possible FTC. As n, the size of the FTC increases beyond two the number of topologically distinct FTCs increases. This is reflected in the increasing number of distinct lines as n increases.

Back to article page