Singularly Impulsive Model of Genetic Regulatory Networks
In this paper we present singular and singularly impulsive model of genetic regulatory networks. Concrete example consists of two gene - two proteins simple synthetic network, and posses two fundamentally present parts in biochemical networks - positive and negative feedback loops. These are important structural parts of biochemical networks and are interesting for control theoreticians. By investigating purpose of positive and negative feedback presence, we see for example that they lead either to bistability (or multistability, in general) in case of positive feedback or generate oscillatory behaviour in case of negative feedback what we show. Mathematical model is derived in form of nonlinear two dimensional dynamical system which is further approximated to singular and singularly impulsive dynamical system. Importance of this example is singular systems approximation which in this particular example leads to interesting and well known phenomena -of relaxation oscillation. This phenomena is consequence of multiple-scale network, i.e. fast-slow decomposition. Jump phenomena that appears as a consequence of time scale differences is very different from jumps (impulsive behaviour) that we have in impulsive systems approximation of, for example, sigmoidal function response by piece-wise linear function in order to reduce complexity.
Nata(s)a A. Kablar Vlada Kvrgi(c) Dragomir Ili(c)
Lola Institute, Kneza Viseslava 70a Belgrade11000, Serbia nkablar Lola Institute, Kneza Viseslava 70a Belgrade 11000, Serbia nkablar
国际会议
The 24th Chinese Control and Decision Conference (第24届中国控制与决策学术年会 2012 CCDC)
太原
英文
113-117
2012-05-23（万方平台首次上网日期，不代表论文的发表时间）