A 5-D hyperchaotic Rikitake dynamo system with hidden attractors

The European Physical Journal Special Topics - Tập 224 Số 8 - Trang 1575-1592 - 2015
Sundarapandian Vaıdyanathan1, Viet–Thanh Pham2, Christos Volos3
1Vel Tech University
2Hanoi University of Science and Technology#TAB#
3Aristotle University of Thessaloniki

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E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)

O.E. Rössler, Phys. Lett. A 57, 397 (1976)

A. Arneodo, P. Coullet, C. Tresser, Commun. Math. Phys. 79, 573 (1981)

G. Chen, T. Ueta, Int. J. Bifur. Chaos 9, 1465 (1999)

J. Lü, G. Chen, Int. J. Bifur. Chaos 12, 659 (2002)

H.K. Chen, C.I. Lee, Chaos Solitons Fractals 21, 957 (2004)

A.M. Harb, Chaos Solitons Fractals 19, 1217 (2004)

G. Tigan, D. Opris, Chaos Solitons Fractals 36, 1315 (2008)

Z. Elhadj, J. Syst. Sci. Complex. 21, 67 (2008)

Q.C. Yang, G.R. Chen, Int. J. Bifurc. Chaos. 18, 1393 (2008)

J. Wang, Z. Chen, Z. Yuan, Chaos Solitons Fractals 42, 3053 (2009)

J. Zhang, W. Tang, Chaos Solitons Fractals 42, 2181 (2009)

V. Sundarapandian, I. Pehlivan, Math. Comput. Model. 55, 1904 (2012)

S. Vaidyanathan, Far. East. J. Math. Sci. 79, 135 (2013)

S. Vaidyanathan, J. Eng. Sci. Technol. Rev. 6, 53 (2013)

S. Vaidyanathan, K. Madhavan, Int. J. Con. The. Appl. 6, 121 (2013)

S. Vaidyanathan, Far. East. J. Math. Sci. 84, 219 (2014)

S. Vaidyanathan, Int. J. Model. Identif. Control 22, 41 (2014)

S. Vaidyanathan, Eur. Phys. J. Special Topics 223, 1519 (2014)

S. Vaidyanathan, Ch Volos, V.T. Pham, K. Madhavan, B.A. Idowu, Arch. Con. Sci. 24, 257 (2014)

S. Vaidyanathan, Int. J. Con. The. Appl. 7, 1 (2014)

S. Vaidyanathan, Ch.K. Volos, V.T. Pham, Stud. Comput. Intel. 576, 571 (2015)

S. Vaidyanathan, A.T. Azar, Stud. Comput. Intel. 581, 59 (2015)

J. Wei, Phys. Lett. A 376, 102 (2011)

S. Jafari, J.C. Sprott, S.M.R.H. Golpayegani, Phys. Lett. A 377, 699 (2013)

X. Wang, G. Chen, Commun. Nonlin. Sci. Num. Simul. 17, 1264 (2012)

G. Leonov, N. Kuznetsov, O. Kuznetsova, S. Seldedzhi, V. Vagaitsev, Trans. Syst. Contr. 6, 54 (2011)

G. Leonov, N. Kutznetsov, V. Vagaitsev, Phys. D 241, 1482 (2012)

N. Smaoui, A. Karouma, M. Zribi, Comm. Nonlin. Sci. Numer. Simul. 16, 3279 (2011)

T.I. Chien, T.L. Liao, Chaos Solitons Fractals 24, 241 (2005)

X. Wu, C. Bai, H. Kan, Comm. Nonlin. Sci. Numer. Simul. 19, 1884 (2014)

Q. Zhang, L. Guo, X. Wei, Optik 124, 3596 (2013)

G. Ye, J. Zhou, Appl. Soft. Comput. 22, 351 (2014)

H. Liu, X. Wang, A. Kadir, Optik 124, 3257 (2013)

O.E. Rössler, Phys. Lett. A 71, 155 (1979)

Q. Jia, Phys. Lett. A 366, 217 (2007)

A. Chen, J. Lu, J. Lü, S. Yu, Phys. A 364, 103 (2006)

X. Li, Commun. Theo. Phys. 52, 274 (2009)

S. Vaidyanathan, Int. J. Con. The. Appl. 6, 97 (2013)

S. Vaidyanathan, Int. J. Cont. Theo. Appl. 7, 35 (2014)

S. Vaidyanathan, Ch.K. Volos, V.T. Pham, Arch. Contr. Sci. 24, 409 (2014)

S. Vaidyanathan, Ch.K. Volos, V.T. Pham, K. Madhavan, Arch. Contr. Sci. 25, 5 (2015)

T. Kapitaniak, K.-E. Thylwe, I. Cohen, J. Wojewoda, Phy. Rev. E 5, 2001 (1995)

T. Kapitaniak, Yu. Maistrenko, S. Popovich, Phy. Rev. E 62, 1972 (2000)

S. Yanchuk, T. Kapitaniak, Phys. Lett. A 290, 139 (2001)

S. Yanchuk, T. Kapitaniak, Phy. Rev. E 64, 056235 (2001)

V. Sundarapandian, Far. East. J. Math. Sci. 42, 289 (2010)

S. Vaidyanathan, Commmun. Comput. Inform. Sci. 131, 585 (2011)

S. Vaidyanathan, Commmun. Comput. Inform. Sci. 198, 1 (2011)

G. Chen, Appl. Math. Comput 217, 7258 (2011)

V. Sundarapandian, Lect. Notes Electr. Eng. 131, 319 (2013)

S. Vaidyanathan, Adv. Intel. Syst. Comput. 177, 1 (2013)

M.T. Yassen, Chaos Solitons Fractals 27, 537 (2006)

J.A. Laoye, U.E. Vincent, S.O. Kareem, Chaos Solitons Fractals 39, 356 (2009)

S. Vaidyanathan, Int. J. Con. The. Appl. 5, 15 (2012)

S. Vaidyanathan, Int. J. Control Theo. Appl. 5, 117 (2012)

L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990)

S. Vaidyanathan, S. Rasappan, Commun. Comput. Inform. Sci. 102, 20 (2010)

P. Sarasu, V. Sundarapandian, Int. J. Syst. Sig. Cont. Eng. Appl. 4, 26 (2011)

V. Sundarapandian, R. Karthikeyan, J. Eng. Appl. Sci. 7, 254 (2012)

S. Vaidyanathan, K. Rajagopal, Commun. Comput. Inform. Sci. 205, 193 (2011)

V. Sundarapandian, R. Karthikeyan, Eur. J. Sci. Res. 64, 94 (2011)

P. Sarasu, V. Sundarapandian, Eur. J. Sci. Res. 72, 504 (2012)

P. Sarasu, V. Sundarapandian, Int. J. Soft Comput. 7, 146 (2012)

C.K. Zhang, L. Jiang, Y. He, Q.H. Wu, M. Wu, Commun. Nonlin. Sci. Numer. Simul. 18, 2743 (2013)

X. Xiao, L. Zhou, Z. Zhang, Commun. Nonlin. Sci. Num. Simul. 19, 2039 (2014)

S. Rasappan, S. Vaidyanathan, Far East J. Math. Sci. 67, 265 (2012)

S. Rasappan, S. Vaidyanathan, Arch. Cont. Sci. 22, 343 (2012)

R. Suresh, V. Sundarapandian, Far East J. Math. Sci. 73, 73 (2013)

S. Vaidyanathan, S. Rasappan, Arabian J. Sci. Eng. 39, 3351 (2014)

V. Sundarapandian, S. Sivaperumal, Int. J. Soft Comput. 6, 224 (2011)

S. Vaidyanathan, S. Sampath, Int. J. Automation Comput. 9, 274 (2012)

S. Vaidyanathan, Int. J. Model. Identific. Con. 22, 170 (2014)

S. Vaidyanathan, A.T. Azar, Stud. Comput. Intel. 576, 527 (2015)

T. Rikitake, Proc. Cambridge Philosoph. Soc. 54, 89 (1958)

A.E. Cook, P.H. Roberts, Proc. Cambridge Philosoph. Soc. 68, 547 (1970)

H.K. Khalil, Nonlin. Syst., 2nd edn. (Prentice Hall, New Jersey, USA, 2001)