Figure 12

(A) Detailed bifurcation diagram of the reduced Wilson model (instantaneous inhibition dynamics, \(\tau _{I} \to 0\) in Eq. (1)) with fixed inputs varying adaptation strength h at \(g=1.5\). The dotted green line shows the assumed location of a branch segment that proved difficult to compute due to the orbits having large period. All complex dynamical behaviors still persist: (B) Mixed-mode oscillations (MMOs) with discontinuous transitions between segments. On MMO branches n:m defines the n high to m low-amplitude oscillations ratio. The number of low-amplitude oscillations starts from one and is increased by one as we move down the bifurcation parameter. (C) Low amplitude winner-take-all (LAWTA) oscillations emerge from Hopf bifurcation on the WTA branch and by further increasing the bifurcation parameter, a cascade of period-doubling bifurcations emerges. Panels B and C show the maximum of \(E_{1} \) & \(E_{2} \) on the limit cycle branches