In the first part of this chapter, we do a local stability and robustness analysis of a model of cyclic biological network representing GRNs (Gene Regulatory Networks) under positive feedback. We present conditions leading to bistable behavior. In the second part, we analyze the GRN under negative feedback. Our analysis depends on an extension of the so-called secant condition, which gives a local stability condition. We deduce conditions leading to global stability of the network.
|Original language||English (US)|
|Title of host publication||Time Delay Systems|
|Subtitle of host publication||Theory, Numerics, Applications, and Experiments|
|Editors||Tamás Insperger, Tulga Ersal, Gábor Orosz|
|State||Published - Apr 1 2017|
|Name|| Advances in Delays and Dynamics|