Abstract
This paper puts forward the control of chaos in the biological system. A new controller based on recursive backstepping sliding mode control is proposed such that it can control the chaotic dynamics in the biological system to stabilize at any position or to track any trajectory that is a smooth function of time. A proportional integral switching surface is proposed to achieve the stability condition of the error dynamics. Unlike the open loop and open plus closed loop control techniques, the design of proposed controller does not require the parameter perturbation. The required stability condition is derived based on Lyapunov stability theory. Simulation is achieved in MATLAB environment. Numerical simulation results are presented in order to show the effective verification of the proposed controller design. Simulation results correspond that the objective of chaos control is achieved successfully.
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References
H. Frohlich, Int. J. Quantum Chem. 2, 641 (1968)
H. Frohlich, F. Kremer, in Coherent Excitations in Biological Systems (Springer-Verlag, Berlin, Heidelberg, NewYork, 1983), pp. 101–142
Fr. Kaiser, Z. Naturforsch. 33, 294 (1978)
S. Jafari, S.M.R.H. Golpayegani, A.H. Jafari, S. Gharibzadeh, Int. J. Gen. Syst. 41, 329 (2012)
S. Jafari, S.M.R.H. Golpayegani, M.R. Darabad, Commun. Nonlinear Sci. Numer. Simul. 18, 811 (2013)
S. Jafari, S.M.R.H. Golpayegani, A.H. Jafari, S. Gharibzadeh, J. Neuropsychiatry Clin. Neurosci. 25, E19 (2013)
S. Jafari, S.M.R.H. Golpayegani, S. Gharibzadeh, Front. Comput. Neurosci. 7, 1 (2013)
Y. Shekofteh, S. Jafari, J.C. Sprott, S.M.R.H. Golpayegani, S. Gharibzadeh, F. Almasganj, Commun. Nonlinear Sci. Numer. Simul. 20, 469 (2015)
S. Aberneth, R.J. Gooding, Physica A 507, 268 (2018)
Fr. Kaiser, Radio Sci. 17, 17S (1982)
H. Frohlich, in Modern Bioelectrochemistry (Plenum Press, New York, 1986), p. 221
H.G. Enjieu Kadji, J.B. Chabi Orou, R. Yamapi, P. Woafo, Chaos Soliton. Fract. 32, 862 (2007)
C.H. Miwadinou, A.V. Monwanoua, J. Yovoganc, L.A. Hinvia, P.R. Nwagoum Tuwae, J.B. Chabi Oroua, Chin. J. Phys. 56, 1089 (2018)
H. Resat, L. Petzold, M.F. Pettigrew, Methods Mol. Biol. 541, 311 (2009)
N.B. Janson, Contemp. Phys. 20, 1 (2010)
R. Testylier, T. Dang, EPTCS 92, 16 (2010)
J. Preto, M. Pettini, HAL Archives ID: hal-00662717 (2012)
S. Motta, F. Pappalardo, Brief. Bioinform. 14, 411 (2012)
V. Gorodetskyi, M. Osadchuk, Phys. Lett. A 377, 703 (2013)
S. Singh, N. Kapoor, Adv. Biol. 2014, 703 (2014)
F. Battiston, Chaos 27, 047404 (2017)
Y. Scharf, Chaos Soliton. Fract. 95, 42 (2017)
U. Deichmann, Chaos Soliton. Fract. 99, 1 (2017)
M. F. Danca, N. Kuznetsov, Chaos Solitons Fract. 103, 144 (2017)
P.S. Shabestari, S. Panahi, B. Hatef, S. Jafari, J.C. Sprott, Chaos Solitons Fract. 112, 44 (2018)
H. Shang, Z. Jiang, R. Xu, D. Wang, P. Wu, Y. Chen, Cogn. Syst. Res. (2018), https://doi.org/10.1016/j.cogsys.2018.04.009
U.E. Vincent, Phys. Lett. A 343, 133 (2005)
P. P. Singh, J. P. Singh, B. K. Roy, IETE J. Res. 63, 1 (2017)
P.P. Singh, B.K. Roy, Ann. Rev. Control 45, 152 (2018)
P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Appl. 8, 995 (2015)
P.P. Singh, J.P. Singh, B.K. Roy, Chaos Soliton. Fract. 69, 31 (2014)
P.P. Singh, J.P. Singh, B.K. Roy, IFAC Proc. 47, 287 (2014)
C.C. Kong, S.H. Chen, Chin. Phys. B 18, 91 (2009)
P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Appl. 9, 171 (2016)
M. Kristic, I. Kanellakopoulos, P. Kokotovic, in Nonlinear and Adaptive Control Design (John Willey and Sons Inc., New York, 1995), pp. 221–248
P.P. Singh, B.K. Roy, in Nonlinear Systems: Design, Applications and Analysis (Nova Science Publishers, New York, 2007), pp. 101–146
P.P. Singh, J.P. Singh, B.K. Roy, Res. Rev.: J. Phys. 3, 1 (2014)
X. Tan, J. Zhang, Y. Yang, Chaos Soliton. Fract. 16, 37 (2003)
U.E. Vincent, A.N. Njah, J.A. Laoye, Physica D 231, 130 (2007)
M. T. Yassen, Chaos Soliton. Fract. 27, 537 (2006)
B.A. Idowu, U.E. Vincent, A.N. Njah, Int. J. Nonlinear Sci. 5, 11 (2008)
S. Mascolo, in Proceedings of the 36IEEE CDC San Diego (2008), Vol. 5, p. 150
M.K. Shukla, B.B. Sharma, Chaos Soliton. Fract. 98, 56 (2017)
P.P. Singh, B.K. Roy, H. Handa, in Ann. IEEE India Conf. (INDICON), Bombay (2013) Vol. 10, pp. 1–6
P.P. Singh, B.K. Roy, in Proceedings of Indian Control Conference (ICC), Kanpur (2015) Vol. 1, pp. 108–111
F Wang, C. Liu, Physica D 225, 55 (2007)
Y. P. Tian, X. Yu, J. Franklin Institute 337, 771 (2009)
B.A. Idowu, U.E. Vincent, A.N. Njah, Chaos Soliton. Fract. 39, 2322 (2009)
D. Swaroop, J.K. Hedrick, P.P. Yip, J.C. Gerdes, IEEE Trans. Autom. Control 45, 1893 (2012)
H.J. Freund, Phys. Rev. E 63, 387 (1983)
W. Singer, C. Gray, Annu. Rev. Neurosci. 18, 555 (1995)
S.J. Schiff, K. Jerger, D.H. Duong, T. Chang, M.L. Spano, W.L. Ditto, Nature 370, 615 (1994)
E.A. Jackson, I. Grosu, Physica D 85, 1 (1995)
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Singh, P.P., Singh, K.M. & Roy, B.K. Chaos control in biological system using recursive backstepping sliding mode control. Eur. Phys. J. Spec. Top. 227, 731–746 (2018). https://doi.org/10.1140/epjst/e2018-800023-6
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DOI: https://doi.org/10.1140/epjst/e2018-800023-6