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. 2011 Oct 27;7(10):e1002248. doi: 10.1371/journal.pcbi.1002248

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Hayut et al.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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Synaptic parameters are as in Figure 12. (A) The bifurcation diagram of the fast subsystem is presented by plotting M _R as a function of the parameter u _LR. Solid black lines denote branches of stable fixed points; M _L = 0 on the upper line and M _F = 0 on the lower line. The points and (Equations 31, 32) are denoted by black solid circles. The green line denotes the slow nullcline of Equation 30, u _LR = CM _R/(1+CM _R). The red line denotes the projection of the limit cycle of the full dynamical system (Equations 1, 3–6) on the M _R–u _LR plane. Parameters: I _R = 0.29, I _F = 0.232. (B) Phase diagram of the RS-LTS-FS network in the I _R−I _F plane. The network exhibits slow network oscillations in the grey area. Outside of this regime, the network reaches a steady state with constant M _R, M _L, and M _F. The LTS and FS populations are quiescent to the left of the black line. To the right of the black line and below the blue line, M _F = 0 and M _L>0. To the right of the black line and to the left and above the green line, M _L = 0 and M _F>0. To the right of the green line and above the red line, M _L>0 and M _F>0.

Inline graphic — Synaptic parameters are as in Figure 12. (A) The bifurcation diagram of the fast subsystem is presented by plotting M _R as a function of the parameter u _LR. Solid black lines denote branches of stable fixed points; M _L = 0 on the upper line and M _F = 0 on the lower line. The points and (Equations 31, 32) are denoted by black solid circles. The green line denotes the slow nullcline of Equation 30, u _LR = CM _R/(1+CM _R). The red line denotes the projection of the limit cycle of the full dynamical system (Equations 1, 3–6) on the M _R–u _LR plane. Parameters: I _R = 0.29, I _F = 0.232. (B) Phase diagram of the RS-LTS-FS network in the I _R−I _F plane. The network exhibits slow network oscillations in the grey area. Outside of this regime, the network reaches a steady state with constant M _R, M _L, and M _F. The LTS and FS populations are quiescent to the left of the black line. To the right of the black line and below the blue line, M _F = 0 and M _L>0. To the right of the black line and to the left and above the green line, M _L = 0 and M _F>0. To the right of the green line and above the red line, M _L>0 and M _F>0.