Saint Petersburg/AlgebraJP


Bistable behaviour of two repressors, mutually repressing each other

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Bifurcation set in (J, P) cross section is given by the following parametric equations:

Spb eqn 028.gif

To obtain the bifurcation curve one should plot the second parameter versus the first, varying X from 0 to P+J. The cusp is located as shown in the figure below. While Q is increasing the cusp tip moves right and upwards.

Bifurc JP1.gif

Important findings:

At constant value of Q and increasing values of P the behaviour changes in the following way:

  • Small P – monostable behaviour
  • Intermediate P – Shmitt trigger/comparator
  • Large P – true trigger (sensitivity increase as P increase)
  • Very large P – monostable behaviour

See also:

(P,Q)-Cross Section - analysis of hysteresis existense

(J,Q)-Cross Section - type of responce at various values of Q