The Complexity of Dynamics in Small Neural Circuits
Fig 5
Relation between any pair of inhibitory membrane potentials in the network.
This figure is obtained for JII = −100 by plotting the four solutions [μI,j]0,1,2,3 of Eqs (14) + (15) (see S1 Text for their analytical calculation) as a function of μI,i, and proves the formation of three branches of solutions of the stationary membrane potentials at the branching-point bifurcations. For example, in the case NI = 2 (left panel), the bisector of the first and third quadrants μI,j = μI,i represents the primary branch of the network, while the other two solutions that bifurcate from the branching points represent the secondary branches. The coordinates of the branching points are given by Eq (23). For the sake of clarity, we do not show the stability of the solutions, which is examined in the text. Moreover, the figure shows that for increasing N these bifurcations disappear, as we discuss in more detail in S1 Text.