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- W197250232 abstract "In this paper we examine the localization problem of compact invariant sets of nonlinear time-varying systems with the di®erentiable right-side. We extend our results respecting the localization problem obtained earlier for time-invariant systems and apply them to a viral infection model. Dynamical properties of the viral infection model is nowadays an intensively studied topic, see e.g. in [1] and references therein. In this paper we examine equations of the viral infection model _ x = i dx i xy; (1) _ y = xy i ay i p(t)yz; _ z = cy i bz; x(0) > 0; y(0) > 0; z(0) > 0; see [1]. Here x(t) describes susceptible host cells, y(t) is the virus population and z(t) is a CTL response. The coe±cient p(t) expresses the strength of the lytic component, which is a general continuous positive periodic nonzero function of time. The main purpose of this paper is to extend previous results of authors on the localization of all compact invariant sets of nonlinear time-invariant systems and apply them to a viral infection model. Here by a localization we mean a description of a set containing all compact invariant sets of the system (1) in terms of equalities and inequalities de ned in the state space R = f (x1; x2; x3) g : Our approach is based on using the rst order extremum conditions. Consider the nonlinear C i di®erentiable time-varying system _ x = f (x; t); f (x; t) = (f1(x; t); : : : ; fn(x; t)) T ; (2)" @default.
- W197250232 created "2016-06-24" @default.
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- W197250232 date "2007-01-01" @default.
- W197250232 modified "2023-09-27" @default.
- W197250232 title "ESTIMATION OF THE DOMAIN CONTAINING ALL COMPACT INVARIANTSETS OF THE VIRAL INFECTION MODEL" @default.
- W197250232 hasPublicationYear "2007" @default.
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