Characterisation of Singular Domains in Threshold-Dependent Biological Networks

Threshold-dependent networks behave like piecewise smooth system which belongs to a class of systems with discontinuous right hand side. It can be studied linear differential equations. At threshold values and their intersections, known as switching boundaries surfaces, the state such is not defined because singularity at points. These states are termed singular or domains network. This study characterise, in terms number, any order network total number domains. shall also propose new definitions for walls one. The definition, derives from Fillipov’s First Order Theory on characterisation (sliding) wall, shown prove better than existing ones it reveal intrinsic behaviours networks.