# MUTANT

A linear, three-dimensional model of a mutant of V. *fischeri*
[1].

Let *x*_{1}, *x*_{2} and *x*_{3} respectively represent the protein *LuxI*, the autoinducer *Ai*
and the complex *Co* described in the original paper. The model has two modes with dynamics in the form
*x'=Ax+b*_{i}, *i=1,2*, where *x=(x*_{1},x_{2},x_{3})^{T} and

*
A=[
-1/3600 0 0;
7.5e-5 -(1/36000+7.5e-9) 1.5e-9;
0 0.005 -1/3600-0.01]
*

and *b*_{1}=(0.00375,0,0)^{T} and *b*_{2}=(3.75375,0,0)^{T}.

We set the state space to be *[0,30000]×[0,60000]×[0,30000]* and the switches occur
when the plane *x*_{3}=1000 is reachable and *x*_{2} in [1000,45000]. We want to verify that
*x*_{1} >= 27500\/x_{2} >= 50000\/x_{3} >= 25000 cannot be reachable when
starting from *[17500,20000]×[40000,45000]×[5000, 7500]* in mode *1*.

Input file