×
Mahmoud, Gamal M.; Ahmed, Mansour E.; Mahmoud, Emad E.

Analysis of hyperchaotic complex Lorenz systems. (English) Zbl 1170.37311

Int. J. Mod. Phys. C 19, No. 10, 1477-1494 (2008).
Summary: 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.

Cited in 36 Documents

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Keywords:

Dynamics; complex; hyperchaotic; chaotic; Lyapunov exponent; Lyapunov dimension; stability; fixed points; bifurcation; periodic; quasi-periodic (2-tours)
PDFBibTeX XMLCite
\textit{G. M. Mahmoud} et al., Int. J. Mod. Phys. C 19, No. 10, 1477--1494 (2008; Zbl 1170.37311)
Full Text: DOI

References:

[1] DOI: 10.1016/0167-2789(82)90057-4 · Zbl 1194.37039 · doi:10.1016/0167-2789(82)90057-4
[2] DOI: 10.1016/0167-2789(83)90123-9 · Zbl 1194.76087 · doi:10.1016/0167-2789(83)90123-9
[3] Ning C. Z., Phys. Rev. A 41 pp 3827–
[4] Kiselev A. D., J. Phys. Stud. 2 pp 30–
[5] DOI: 10.1016/S0167-2789(96)00129-7 · Zbl 0887.34048 · doi:10.1016/S0167-2789(96)00129-7
[6] DOI: 10.1142/S0129183107010425 · Zbl 1115.37035 · doi:10.1142/S0129183107010425
[7] Mahmoud G. M., Int. J. Bifurcat. Chaos 17
[8] DOI: 10.1007/s11071-007-9200-y · Zbl 1170.70365 · doi:10.1007/s11071-007-9200-y
[9] DOI: 10.1142/S0218127404011624 · Zbl 1091.34524 · doi:10.1142/S0218127404011624
[10] DOI: 10.1016/0167-2789(85)90176-9 · Zbl 0579.76051 · doi:10.1016/0167-2789(85)90176-9
[11] DOI: 10.1103/PhysRevLett.76.904 · doi:10.1103/PhysRevLett.76.904
[12] Li Y., IEEE T. CAS 52 pp 204–
[13] DOI: 10.1142/S0218127403008284 · Zbl 1057.37026 · doi:10.1142/S0218127403008284
[14] DOI: 10.1080/002071799220614 · Zbl 0989.93069 · doi:10.1080/002071799220614
[15] DOI: 10.1016/j.physleta.2007.02.024 · Zbl 1203.93086 · doi:10.1016/j.physleta.2007.02.024
[16] Li Y., Dynam. Cont. Dis. Ser. B 14 pp 97–
[17] DOI: 10.1016/j.physleta.2006.10.044 · Zbl 1197.34107 · doi:10.1016/j.physleta.2006.10.044
[18] DOI: 10.1016/j.physa.2005.09.039 · doi:10.1016/j.physa.2005.09.039
[19] DOI: 10.1016/j.physleta.2007.05.028 · Zbl 1209.93105 · doi:10.1016/j.physleta.2007.05.028
[20] DOI: 10.1103/PhysRevLett.91.034101 · doi:10.1103/PhysRevLett.91.034101
[21] DOI: 10.1088/0031-8949/77/02/025001 · Zbl 1141.37016 · doi:10.1088/0031-8949/77/02/025001
[22] Barrio R., Physica D 299 pp 43–
[23] DOI: 10.1016/j.physleta.2007.11.067 · Zbl 1220.37013 · doi:10.1016/j.physleta.2007.11.067
[24] DOI: 10.1016/j.chaos.2006.05.030 · doi:10.1016/j.chaos.2006.05.030
[25] DOI: 10.1142/S0218127407019950 · Zbl 1143.37309 · doi:10.1142/S0218127407019950
[26] Frederickson P., J. Diff. Eq. 44 pp 185–
[27] Shuster H. G., Deterministic Chaos (1982)
[28] DOI: 10.1002/9783527617548 · doi:10.1002/9783527617548
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.