Figure 2

Dynamics of a single unit. Graphical description of the dynamical system defined by Equation 1. (a): Bifurcation diagram in the parameter λ. The vertical dotted lines mark the parameter values corresponding to the bifurcation points in the system, λ = 0 and λ = 1. The straight horizontal line represents the fixed point which exists at the origin, z = 0, for all values of λ. The fixed point is attracting for λ < 1 (solid line) and repelling otherwise (dashed line). The two pairs of curved lines represent the two limit-cycles in this system. The fixed point becomes unstable at the HP point, HP, at which point the unstable limit-cycle (curved dashed lines) is born. There is also a stable limit-cycle (curved solid lines). The two limit-cycles are joined by a limit-point, LP. (b): Two timeseries (dotted lines) of the system with different initial conditions and 0 < λ < 1. One trajectory begins just outside the unstable limit-cycle and the other just inside. The two trajectories quickly diverge with one heading towards the fixed point and the other towards the outer limit-cycle. (c): Same two trajectories (dotted lines) in the phase plane. The solid and dotted lines in panels (b, c) mark the positions of the stable and unstable limit-cycles, respectively.