© The Institution of Engineering and Technology
A mathematical model of a tumour growth cancer cell is investigated. A simple analogue circuit for mimicking the tumour growth cancer cell model is constructed for the first time. The stability of the proposed system is studied. The familiar chaos control technique, i.e. the non-feedback loop is performed to control the chaotic behaviour. The possible application of this study is discussed.
References
-
-
1)
-
5. Anderson, A.R., Chaplain, M.A.J.: ‘Continuous and discrete mathematical models of tumor-induced angiogenesis’, Bull. Math. Biol., 1998, 60, p. 857 (doi: 10.1006/bulm.1998.0042).
-
2)
-
8. Lakshmanan, M., Murali, K.: ‘Chaos in nonlinear oscillators: controlling and synchronization’ (World Scientific Publishing, Singapore, 1996).
-
3)
-
3. Ivancevic, T.T., Bottema, M.J., Jain, L.C.: ‘A mathematical model of chaotic attractor in tumor growth and decay’, , 2008.
-
4)
-
9. Ott, E., Grebogi, C., Yorke, J.A.: ‘Controlling chaos’, Phys. Rev. Lett., 1990, 64, p. 1196 (doi: 10.1103/PhysRevLett.64.1196).
-
5)
-
2. Sun, J.D., Liu, Q., Wang, J., et al: ‘Selective tumor hypoxia targeting by hypoxia-activated prodrug TH-302 inhibits tumor growth in preclinical models of cancer’, Clin. Cancer Res., 2012, 18, p. 758 (doi: 10.1158/1078-0432.CCR-11-1980).
-
6)
-
1. Merlo, L.M., Pepper, J.W., Reid, B.J., et al: ‘Cancer as an evolutionary and ecological process’, Nat. Rev. Cancer, 2006, 6, p. 924 (doi: 10.1038/nrc2013).
-
7)
-
4. Roose, T., Chapman, S.J., Maini, P.K.: ‘Mathematical models of avascular tumor growth’, SIAM Rev., 2007, 49, p. 179 (doi: 10.1137/S0036144504446291).
-
8)
-
6. Ramis-Conde, I., Chaplain, M.A., Anderson, A.R.: ‘Mathematical modelling of cancer cell invasion of tissue’, Math. Comput. Model., 2008, 47, p. 533 (doi: 10.1016/j.mcm.2007.02.034).
-
9)
-
7. Georg, A.G., Melbourne, I.: ‘A new test for chaos in deterministic systems’, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society, 2004, 460, (2042), p. 603 (doi: 10.1098/rspa.2003.1183).
http://iet.metastore.ingenta.com/content/journals/10.1049/el.2018.5126
Related content
content/journals/10.1049/el.2018.5126
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Correspondence
This article has following corresponding article(s):
interview