Fig. 2

Six planar bifurcations are responsible for oscillation onset and offset. In a dynamical system, a bifurcation occurs when a smooth change of the values of some of the parameters of the system causes a sudden qualitative change of its behavior. The parameters that need to be varied to have this change in behavior are called bifurcation parameters. The number of bifurcation parameters necessary gives the codimension of the bifurcation. In planar systems, only six types of codim-1 bifurcations can cause the transition from silent (stable fixed point, FP) to oscillatory (limit cycle, LC) behavior and/or vice versa. Their characteristics are illustrated in this figure. For each bifurcation we report an example of how the state space changes when varying the bifurcation parameter p. Bifurcations occur at the critical value \(p_{c}\). Stable, saddle, unstable fixed points are represented by full, empty with a line inside, empty gray dots, respectively. Stable, half-stable, unstable limit cycles are shown with solid, dotted, dashed lines, respectively. Orbits appear in blue. We also show an example of timeseries and report the amplitude–frequency behavior, where \(\lambda=p-p_{c}\). In the second last column we state whether the stable fixed point is inside or outside the stable limit cycle. This can affect the behavior of the baseline in the timeseries. The last column indicates the reversibility of the bifurcation, in the direction of the FP to the LC