The model was initially proposed in a paper from Laub and Loomis [1], and then studied by several papers in reachability computation such as [2], [3]. The dynamics of the model is defined by

We firstly consider a small initial set which is given by

The following figures shows the interval overapproximations of the flowpipes in the time horizon [0,20] computed by Flow* 2.1.0. The total time cost is 18 seconds.

For a larger initial set

over the same time horizon, Flow* spends 60 seconds and generates the following result.

### References

[1] M. T. Laub and W. F. Loomis.

*A molecular network that produces spontaneous oscillations in excitable cells of dictyostelium.*

Molecular Biology of the Cell, 9:3521–3532, 1998.

[2] R. Testylier and T. Dang.

*NLTOOLBOX: A library for reachability computation of nonlinear dynamical systems.*

In Proc. of ATVA’13, volume 8172 of LNCS, pages 469–473. Springer, 2013.

[3] X. Chen and S. Sankaranarayanan.

*Decomposed Reachability Analysis for Nonlinear Systems.*

In IEEE Real Time Systems Symposium (RTSS), pp. 13-24, 2016.