# Saint Petersburg/AlgebraJP

### From 2007.igem.org

## Bistable behaviour of two repressors, mutually repressing each other

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

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.

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