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ANALYSIS OF HYPERCHAOTIC COMPLEX LORENZ SYSTEMS

GAMAL M. MAHMOUD

Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt

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MANSOUR E. AHMED

Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt

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, and

EMAD E. MAHMOUD

Department of Mathematics, Faculty of Science, Sohag University, Egypt

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https://doi.org/10.1142/S0129183108013151Cited by:87 (Source: Crossref)

Abstract

This paper introduces and analyzes new hyperchaotic complex Lorenz systems. These systems are 6-dimensional systems of real first order autonomous differential equations and their dynamics are very complicated and rich. In this study we extend the idea of adding state feedback control and introduce the complex periodic forces to generate hyperchaotic behaviors. The fractional Lyapunov dimension of the hyperchaotic attractors of these systems is calculated. Bifurcation analysis is used to demonstrate chaotic and hyperchaotic behaviors of our new systems. Dynamical systems where the main variables are complex appear in many important fields of physics and communications.

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References

A. C. Fowler, M. J. McGuinnes and J. D. Gibbon, Physica D 4, 139 (1982), DOI: 10.1016/0167-2789(82)90057-4. Web of Science, ADS, Google Scholar
A. C. Fowler, J. D. Gibbon and M. J. McGuinnes, Physica D 7, 126 (1983), DOI: 10.1016/0167-2789(83)90123-9. Web of Science, ADS, Google Scholar
C. Z. Ning and H. Haken, Phys. Rev. A 41, 3827 (1990). Google Scholar
A. D. Kiselev, J. Phys. Stud. 2, 30 (1998). Web of Science, Google Scholar
A. Rauh, L. Hannibal and N. B. Abraham, Physica D 99, 45 (1996), DOI: 10.1016/S0167-2789(96)00129-7. Web of Science, ADS, Google Scholar
G. M. Mahmoud, M. A. Al-Kashif and S. A. Aly, Int. J. Mod. Phys. C 18, 253 (2007), DOI: 10.1142/S0129183107010425. Link, Web of Science, ADS, Google Scholar
G. M. Mahmoud, T. Bountis and E. E. Mahmoud, Int. J. Bifurcat. Chaos 17, (2007). Google Scholar
G. M. Mahmoud, S. A. Aly and M. A. Al-Kashif, Nonlinear Dynam. 51, 171 (2008), DOI: 10.1007/s11071-007-9200-y. Web of Science, Google Scholar
G. M. Mahmoud and T. Bountis, Int. J. Bifurcati. Chaos 14, 3821 (2004), DOI: 10.1142/S0218127404011624. Link, Web of Science, Google Scholar
C. A. Jones, N. D. Weiss and F. Cataeno, Physica D 14, 161 (1985), DOI: 10.1016/0167-2789(85)90176-9. Web of Science, ADS, Google Scholar
J. H. Penget al., Phys. Rev. Lett. 76, 904 (1996), DOI: 10.1103/PhysRevLett.76.904. Web of Science, ADS, Google Scholar
Y. Li, G. Chen and W. K. Tang, IEEE T. CAS 52, 204 (2005). Web of Science, Google Scholar
D. Cafagna and G. Grassi, Int. J. Bifur. Chaos 13, 2889 (2003), DOI: 10.1142/S0218127403008284. Link, Web of Science, Google Scholar
J. Y. Hsiehet al., Int. J. Contr. 72, 882 (1999). Web of Science, Google Scholar
Q. Jia, Phys. Lett. A 366, 217 (2007), DOI: 10.1016/j.physleta.2007.02.024. Web of Science, ADS, Google Scholar
Y. Liet al., Dynam. Cont. Dis. Ser. B 14, 97 (2007). Web of Science, Google Scholar
Q. Jia, Phys. Lett. A 362, 424 (2007), DOI: 10.1016/j.physleta.2006.10.044. Web of Science, ADS, Google Scholar
A. Chenet al., Physica A 364, 103 (2006), DOI: 10.1016/j.physa.2005.09.039. Web of Science, ADS, Google Scholar
Q. Jia, Phys. Lett. A 370, 40 (2007), DOI: 10.1016/j.physleta.2007.05.028. Web of Science, ADS, Google Scholar
I. Grigorenko and E. Grigorenko, Phys. Rev. Lett. 91, 034101 (2003), DOI: 10.1103/PhysRevLett.91.034101. Web of Science, Google Scholar
F. Chen, L. Chen and W. Zhang, Phys. Scr. 77, 025001 (2008), DOI: 10.1088/0031-8949/77/02/025001. Web of Science, Google Scholar
R. Barrio and S. Serrano, Physica D 299, 43 (2007). Google Scholar
M. Suzuki, N. Sakamoto and T. Yasukochi, Phys. Lett. A 372, 2614 (2008), DOI: 10.1016/j.physleta.2007.11.067. Web of Science, ADS, Google Scholar
T. Gaoet al., Chaos Soliton Fract. 35, 390 (2008), DOI: 10.1016/j.chaos.2006.05.030. Web of Science, ADS, Google Scholar
R. Barboza, Int. J. Bifur. Chaos 17, 4285 (2007), DOI: 10.1142/S0218127407019950. Link, Web of Science, Google Scholar
P. Fredericksonet al., J. Diff. Eq. 44, 185 (1983). Web of Science, Google Scholar
H. G. Shuster , Deterministic Chaos ( Springer , Berlin , 1982 ) . Google Scholar
A. H. Nayfeh , Applied Nonlinear Dynamics ( Wiley and Sons, Inc. , New York , 1995 ) . Google Scholar
G. M. Mahmoud et al., in preparation . Google Scholar