A class of piecewise linear differential equations arising in biological models

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Validation of qualitative models of genetic regulatory networks by model checking: analysis of the nutritional stress response in Escherichia coli (2005, unknown): “See de Jong et al. (2004) and Gouze and Sari (2002) for a detailed description.”
A Filippov sliding vector field on an attracting co-dimension 2 discontinuity surface, and a limited loss-of-attractivity analysis☆ (2013, background): “[4,5,13,22]; for works on the class of complementarity systems, see [14], for works from the point of view of bifurcations of dynamical-systems see [7,16,15,19]; and, of course, see the classical references [3,11,26,27] for a thorough theoretical introduction to these systems.”
Modeling and Simulation of Genetic Regulatory Systems: A Literature Review (2002, unknown): “In the (cid:142) rst place, the small numbers of molecules of some of the components of the regulatory system compromise the continuity assumption.”
Qualitative simulation of genetic regulatory networks using piecewise-linear models (2004, methodology): “Recently, it has been shown that an approach capable of dealing with differential equations with discontinuous right-hand sides, widely used in control theory, allows the above-mentioned problems to be resolved in a mathematically proper and practically useful manner [31].”