Figure 10

Bifurcation analysis for F&S rivalry. (A) Bifurcation diagram for the Wilson model (1) with high frequency flickering (18 Hz) and low frequency swap (1.5 Hz) varying adaptation strength h at \(g=1.5\). Dynamical behavior for large values of adaptation strength is modulated SIM (SIM-Mod). Cycle skipping behavior appears through period-doubling bifurcation (PD) in which every population only responds to every other stimulus onset in turn. There also exist a pair of stable limit cycles for very small values of adaptation strength which corresponds to modulated WTA (WTA-Mod), not visible at this scale. Solid curve: stable limit cycle, dashed curve: unstable limit cycle. (B) Boundaries of different dynamical behaviors are shown in parameter space \((h,g)\). The region with cycle skipping solution is confined by period-doubling (PD) bifurcations. Other parameters: \([J_{\mathrm{HL}}]_{\max }=[J_{\mathrm{VR}}]_{\max }=10\)