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Stability analysis around singular stationary points and computer algebra systems


A CAS-based method to study asymptotic properties of solutions to systems of differential equations with distributed time-delays and Boolean-type nonlinearities (step functions) is offered. Such systems arise in many applications, but this paper deals with specific examples of such systems coming from genetic regulatory networks. A challenge is to analyze stable stationary points which belong to the discontinuity set of the system (thresholds). In this work we do the stability analysis around such points in the presence of delays. The basic technical tool consists in replacing step functions by the so-called "logoid functions" and investigating the smooth systems thus obtained. The authors would like to thank The Norwegian Programme for Development, Research and Education (NUFU) for partial financial support.


gene regulatory systems; step functions; stability of non-continuous systems

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