Resolution:
## Figure 1.
Signal-response curve (bifurcation diagram) of system (2) for the parameters k_{1 }= 8, k_{2 }= 1, k_{3 }= 1, k_{4 }= 1.5. Solid lines indicate locally stable steady states, the dashed line locally
unstable steady states. The inset shows the signal-response curve if an additional
small constant influx into X (here 0.6) is assumed (enabling a positive 'off' state,
leaving the 'on' state and bifurcation point nearly unchanged). This is the classical
toggle switch (terminology of Tyson et al. (6), others use the term toggle switch
to describe a double negative (i.e. positive) feedback loop (4)) picture enabling
the hysteresis cycle: starting with low values and increasing the signal continuously
increases the response, until the saddle-node bifurcation at about S = 1.7 is reached.
Further increase of the signal leads to a sudden jump of the response to the upper
steady state. Decreasing the signal now leads to a continuous decrease of the response,
the systems stays in the upper steady state until the left bifurcation point is reached
where the response jumps back to the lower steady state.
Wilhelm |