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Figure 8 | The Journal of Mathematical Neuroscience

Figure 8

From: Methods to assess binocular rivalry with periodic stimuli

Figure 8

Bifurcation analysis for swap only case. (A) Bifurcation diagram for the Wilson model (1) with low frequency periodic forcing (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 a 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). Solid curve: stable limit cycle, dashed curve: unstable limit cycle. (B) Detailed bifurcation diagram for the Wilson model with low frequency periodic forcing (swap; 1.5 Hz) varying adaptation strength h at \(g=25\). (C) Multi-cycle skipping occurs through discontinuous branches. The number of cycles skipped between switches increases by one as we move left from one branch segment to the next. (D) A cascade of period-doubling bifurcations that leads to chaos. In panels C and D, the ordinate shows maximum of \(E_{1} \) & \(E_{2} \). (E) Boundaries of different dynamical behaviors with low frequency periodic forcing (swap 1.5 Hz) are shown in parameter space \((h,g)\). The region with the cycle skipping solution is confined by period-doubling (PD) bifurcations from beneath and by fold bifurcation from above (marked with arrows). Other parameters: \([J_{\mathrm{HL}}]_{\max }=[J_{\mathrm{VR}}]_{\max }=10\)

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