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

• Autorzy: Kruthika H. A. , Mahindrakar A. D. , Pasumarthy R.

Identyfikatory

DOI

10.1515/amcs-2017-0007

• 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.

Słowa kluczowe

EN

time delay; cancer immunotherapy; gene regulatory network; sum of squares

PL

opóźnienie czasowe; immunoterapia nowotworowa; sieć regulacyjna genu; suma kwadratów

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2017
• Tom: Vol. 27, no. 1
• Strony: 91--103
• Opis fizyczny: Bibliogr. 39 poz., rys., wykr.

Twórcy

autor

Kruthika H. A.

• Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India

autor

Mahindrakar A. D.

• Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India

autor

Pasumarthy R.

• Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).