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.