New jerk circuits with mixed-mode oscillations

We propose two jerk circuits that can generate mixed-mode oscillations of various sequences. The circuits' responses comprise both the large (L) and small (s) amplitude oscillations which result in a periodic L
^s
sequence. The L
^s
patterns follow the Farey arithmetic when the circuits' parameters bifurcate in certain intervals. One of the two jerk circuits has a Newtonian form as its mathematical model can be derived from the second Newton's law x" = F/m, with x" = d
²
x/dt
²
being an “acceleration” variable. Several PSPICE and Matlab simulation results are included.