On a differential system arising in the network control theory | Zendy

Eduard Brokan | Zendy; Felix Sadyrbaev | Zendy

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On a differential system arising in the network control theory

Author(s) -

Eduard Brokan,

Felix Sadyrbaev

Publication year - 2016

Publication title -

nonlinear analysis modelling and control

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.734

H-Index - 32

eISSN - 2335-8963

pISSN - 1392-5113

DOI - 10.15388/na.2016.5.8

Subject(s) - set (abstract data type) , complement (music) , function (biology) , differential (mechanical device) , computer science , physics , chemistry , thermodynamics , biology , biochemistry , evolutionary biology , complementation , programming language , gene , phenotype

. 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 = ∑ Wijxj − 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 setΩ or to the complement ofΩ or to the boundary of Ω, where Ω is fully defined set.

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