Each of the following videos shows stability analysis of periodically forced canonical oscillators in a different parameter regime. The steady-state amplitude, r*, and relative phase, ψ*, of canonical oscillators are plotted as a function of frequency difference, Ω, for increasing forcing amplitude, F. The color of each fixed point (r*, ψ*) indicates its stability: orange for a stable node, yellow for a stable spiral, light green for an unstable node, light blue for an unstable spiral, and blue for a saddle point.

 

Video 1. Critical Hopf oscillators (α = 0, β₁ = −100, β₂ = 0)

 

 

Video 2. Supercritical Hopf oscillators (α = 1, β₁ = −100, β₂ = 0)

 

 

 

Video 3. Supercritical double limit cycle oscillators (α = -1, β₁ = 4, β₂ = -1, ε = 1)

 

 

Video 4. Subcritical double limit cycle oscillators (α = -1, β₁ = 2.5, β₂ = -1, ε = 1)

 

Reference: Kim, J. C., & Large, E. W. (2015). Signal processing in periodically forced gradient frequency neural networks. Frontiers in Computational Neuroscience. 9:152.