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Figure 3 | The Journal of Mathematical Neuroscience

Figure 3

From: Methods to assess binocular rivalry with periodic stimuli

Figure 3

Bifurcation analysis and time histories for traditional rivalry. (A) Bifurcation diagram for the Wilson model (1) with fixed inputs varying adaptation strength h. Three main types of dynamical behaviors are presented: Winner-takes-all (WTA), Rivalry oscillations (RIV), Simultaneous activity (SIM). Blue lines show fixed point branches and the green line shows the maximum of \(E_{1} \) & \(E_{2} \) on the limit cycle branch. The minimum of RIV branch oscillations is close to zero once away from Hopf bifurcation (not shown). (B) Details of the diagram are shown in a zoomed panel. The period of oscillations on the unstable limit cycle branch shown with green dashed lines increase sharply as we move toward a critical parameter value \(h\approx 4.22843\) and continuation fails. The dotted green line shows the assumed location of a branch segment that proved difficult to compute due to the orbits having large period. The sequence of bifurcations that transform the system from WTA to RIV periodic solutions has not been described previously. (C) Time histories associated with each dynamical behavior: WTA (\(h=1\)), RIV (\(h=4.3\)), SIM (\(h=15\)). Other parameters: \(g=1.5\), \(J_{\mathrm{HL}}=J_{\mathrm{VR}}=10\)

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