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2017 | 27 | 1 | 91-103
Tytuł artykułu

Stability analysis of nonlinear time-delayed systems with application to biological models

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we analyse the local stability of a gene-regulatory network and immunotherapy for cancer modelled as nonlinear time-delay systems. A numerically generated kernel, using the sum-of-squares decomposition of multivariate polynomials, is used in the construction of an appropriate Lyapunov-Krasovskii functional for stability analysis of the networks around an equilibrium point. This analysis translates to verifying equivalent LMI conditions. A delay-independent asymptotic stability of a second-order model of a gene regulatory network, taking into consideration multiple commensurate delays, is established. In the case of cancer immunotherapy, a predator-prey type model is adopted to describe the dynamics with cancer cells and immune cells contributing to the predator-prey population, respectively. A delay-dependent asymptotic stability of the cancer-free equilibrium point is proved. Apart from the system and control point of view, in the case of gene-regulatory networks such stability analysis of dynamics aids mimicking gene networks synthetically using integrated circuits like neurochips learnt from biological neural networks, and in the case of cancer immunotherapy it helps determine the long-term outcome of therapy and thus aids oncologists in deciding upon the right approach.
Rocznik
Tom
27
Numer
1
Strony
91-103
Opis fizyczny
Daty
wydano
2017
otrzymano
2016-04-05
poprawiono
2016-08-20
poprawiono
2016-10-01
zaakceptowano
2016-10-12
Twórcy
  • Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India
  • Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India
  • Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv27i1p91bwm
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