Chaos control in HIV Infection of CD4+ T-cells System by Lie Algebraic Exact Linearization

0*
Assistant Professor, Department of General Requirements, College of Applied Sciences, Nizwa, Oman.
Periodicity:January - March'2016
DOI : https://doi.org/10.26634/jmat.5.1.4868

Abstract

This Paper deals with the control of chaotic dynamics of healthy, infected CD+4 T-cells and free HIV (Human Immunodeficiency Virus) cells in a chaotic system of HIV infection of CD+4 T-cells by implementing a Lie algebraic exact  linearization technique. A nonlinear feedback control law is designed, which induces a co-ordinate transformation thereby changing the original chaotic HIV system into a controlled linear system. Numerical simulation has been carried by using Mathematica that witness the robustness of the technique implemented on the chosen chaotic system.

Keywords

Exact Linearization, Lie Bracket, Lie Derivative, Nonlinear Feedback, HIV Model.

How to Cite this Article?

Shahzad,M. (2016). Chaos control in HIV Infection of CD4+ T-cells System by Lie Algebraic Exact Linearization. i-manager’s Journal on Mathematics, 5(1), 20-30. https://doi.org/10.26634/jmat.5.1.4868

References

[1]. E. Ott, C. Grebogi, and J.A.Yorke, (1990). “Controlling Chaos”. Physical Review Letters, Vol. 64, pp.1196-1204.
[2]. E. Scholl and H.G. Schuster, (1999). Handbook of Chaos Control. Wiley: Weinheim.
[3]. M.I. Rabinovich and H.D.I. Abarbanel, (1998). “The Role of Chaos in Neural Systems”. Neuro Science, Vol.87, pp.5-14.
[4]. S. Steingrube, M. Timme, F.Worg and P. Manoonpong, (2010). “Self-organized Adaptation of a Simple Neural Circuit Enables Complex Robot Behavior”. Nature of Physics, Vol.6, pp.224-230.
[5]. J. Guckenheimer and P. Holmes, (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag: New York.
[6]. M. Vittot, (2004). “Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula”. Journal of Physics A: Mathematical and General, Vol.37, pp.6337-6357.
[7]. A. Khan and M. Shahzad, (2008). “Control of Chaos in Hamiltonian System of Mimas-Tethys System”. The Astronomical Journal, Vol.136, pp.2201-2203.
[8]. M. Islam B. Islam and N. Islam, (2014). “Chaos Control in Shimizu Morioka System by Lie Algebraic Exact Linearization”. International Journal on Dynamics Control, Vol.2, pp.386-394.
[9]. B.R. Andrievskii and A.L. Fradkov, (2003). “Control of Chaos: Methods and Applications”. Automatic Remote Control, Vol.64, pp.673-713.
[10]. L.Q. Chen and Y.Z. Liu, (1999). “A Modified Exact Linearization Control for Chaotic Oscillators”. Nonlinear Dynamics, Vol.20, pp.309-317.
[11]. C. Liqun and L. Yanzhu, (1998). “Control of Lorenz Chaos by the Exact Linearization”. Applied Mathematics and Mechanics, Vol.19, pp.67-73.
[12]. N. Islam, H.P. Mazumdar and A. Das, (2009). “On the Stability and Control of Shimuzu Morioka System of Differential Equations”. Differential Geometry Dynamical Systems, Vol.11, pp.135-143
[13]. N. Islam, B. Islam and H.P. Mazumdar, (2011). “Generalised Chaos Synchronization of Unidirectionally Coupled Shimizu Morioka Dynamical System”. Differential Geometry Dynamical Systems, Vol.13, pp.114-119.
[14]. M. Islam,B. Islam and N. Islam, (2013). “Rate Estimation of Identical Synchronization by Designing Controllers”. Journal of Mathematics, doi:10.1155/2013/590462.
[15]. A. Mondal, N. Islam and S. Sen, (2015). “Control of Chaos in Sprott System by State Space Exact Linearization Method”. International Journal on Mathematics and Computer Science, Vol.1, pp.11-18.
[16]. G.R. Tsagas and H.P. Mazumdar, (2000). “On the Control of a Dynamical System by a Linearization Method via Lie Algebra”. Review of Calcutta Mathematical Society, Vol.8, pp.25-32.
[17]. J. Alvarez-Gallegos, (1994). “Non-linear Regulation of a Lorenz System by Feedback Linearization Techniques”. Dynamic Control, Vol.4, pp.272-289.
[18]. T. Shinbrot, C. Grebogi, E. Ott and J.A. Yorkee, (1993). “Using Small Perturbation to Control Chaos”. Nature, Vol.363, pp.411-474.
[19]. M.R. Jafari, S. Effati and H. Salarabedi, (2012). “Chaos Control and Global Stabilization of HIV Infection of CD T-cells 4 System”. International Journal of Nonlinear Science, Vol.13, pp.446-453.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.