6533b860fe1ef96bd12c31ab
RESEARCH PRODUCT
On a differential system arising in the network control theory
Eduard BrokanFelix Sadyrbaevsubject
PhysicsNetwork controlPure mathematicsnetwork controlPhase portraitattracting setsApplied Mathematics010102 general mathematicslcsh:QA299.6-433Boundary (topology)phase portraitlcsh:Analysis02 engineering and technology01 natural sciencesdynamical systemSet (abstract data type)Matrix (mathematics)Systems theory0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processing0101 mathematicsDynamical system (definition)AnalysisComplement (set theory)description
We investigate the three-dimensional dynamical system occurring in the network regulatory systems theory for specific choices of regulatory matrix { { 0, 1, 1 } { 1, 0, 1 } { 1, 1, 0 } } and sigmoidal regulatory function f(z) = 1 / (1 + e-μz), where z = ∑ Wij xj - θ. The description of attracting sets is provided. The attracting sets consist of respectively one, two or three critical points. This depends on whether the parameters (μ,θ) belong to a set Ω or to the complement of Ω or to the boundary of Ω, where Ω is fully defined set.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-10-10 | Nonlinear Analysis: Modelling and Control |