We consider a genetic model which is adapted from the one described in [1]. The dynamics is defined by the following ODE:
We consider the initial set
and the time horizon [0,3]. The following figures shows the projections of the interval overapproximations of the flowpipes computed by Flow* 2.1.0. The total time cost is about 100 seconds.
References
[1] J. M. G. Vilar, H. Y. Kueh, N. Barkai, and S. Leibler.
Mechanisms of noise-resistance in genetic oscillators.
Proc. of the National Academy of Sciences of the United States of America, 99(9):5988–5992, 2002.
[2] X. Chen and S. Sankaranarayanan.
Decomposed Reachability Analysis for Nonlinear Systems.
In IEEE Real Time Systems Symposium (RTSS), pp. 13-24, 2016.