Abstract：
:A significant conceptual difficulty in the use of switching systems to model regulatory networks is the presence of so-called "black walls," co-dimension 1 regions of phase space with a vector field pointing inward on both sides of the hyperplane. Black walls result from the existence of direct negative self-regulation in the system. One biologically inspired way of removing black walls is the introduction of intermediate variables that mediate the negative self-regulation. In this paper, we study such a perturbation. We replace a switching system with a higher-dimensional switching system with rapidly decaying intermediate proteins, and compare the dynamics between the two systems. We find that the while the individual solutions of the original system can be approximated for a finite time by solutions of a sufficiently close perturbed system, there are always solutions that are not well approximated for any fixed perturbation. We also study a particular example, where global basins of attraction of the perturbed system have a strikingly different form than those of the original system. We perform this analysis using techniques that are adapted to dealing with non-smooth systems.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Fan G,Cummins B,Gedeon Tdoi
10.1007/s11538-016-0175-zsubject
Has Abstractpub_date
2016-06-01 00:00:00pages
1077-120issue
6eissn
0092-8240issn
1522-9602pii
10.1007/s11538-016-0175-zjournal_volume
78pub_type
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