Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers

Lan Zhang; Cheng Jian Zhang

Kybernetika (2008)

  • Volume: 44, Issue: 1, page 35-42
  • ISSN: 0023-5954

Abstract

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A four-dimensional hyperchaotic Lü system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic Lü system well, the chaotic state is transformed to the periodic orbit. Finally, we consider the differences between the analysis of the hyperchaotic Lorenz system, hyperchaotic Chen system and hyperchaotic Lü system.

How to cite

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Zhang, Lan, and Zhang, Cheng Jian. "Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers." Kybernetika 44.1 (2008): 35-42. <http://eudml.org/doc/33910>.

@article{Zhang2008,
abstract = {A four-dimensional hyperchaotic Lü system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic Lü system well, the chaotic state is transformed to the periodic orbit. Finally, we consider the differences between the analysis of the hyperchaotic Lorenz system, hyperchaotic Chen system and hyperchaotic Lü system.},
author = {Zhang, Lan, Zhang, Cheng Jian},
journal = {Kybernetika},
keywords = {Hopf bifurcation; periodic solution; multiple delays and parameters; hyperchaotic Lü system; hyperchaotic Chen system; hyperchaotic Lorenz system; Hopf bifurcation; periodic solution; multiple delays and parameters; hyperchaotic Lü system; hyperchaotic Chen system; hyperchaotic Lorenz system},
language = {eng},
number = {1},
pages = {35-42},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers},
url = {http://eudml.org/doc/33910},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Zhang, Lan
AU - Zhang, Cheng Jian
TI - Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 1
SP - 35
EP - 42
AB - A four-dimensional hyperchaotic Lü system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic Lü system well, the chaotic state is transformed to the periodic orbit. Finally, we consider the differences between the analysis of the hyperchaotic Lorenz system, hyperchaotic Chen system and hyperchaotic Lü system.
LA - eng
KW - Hopf bifurcation; periodic solution; multiple delays and parameters; hyperchaotic Lü system; hyperchaotic Chen system; hyperchaotic Lorenz system; Hopf bifurcation; periodic solution; multiple delays and parameters; hyperchaotic Lü system; hyperchaotic Chen system; hyperchaotic Lorenz system
UR - http://eudml.org/doc/33910
ER -

References

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  6. Olien L., Belair J., Bifurcation, stability and monotonicity properities of a delayed neural network model, Physica D 102 (1997), 349–363 (1997) MR1439692
  7. Heyes N. D., Linear autonomous neutral functional differential equations, J. Differential Equations 15 (1974), 106–128 (1974) MR0338520
  8. Jia Q., Hyperchaos generated from the Lorenz chaotic system and its control, Phys. Lett. A 366 (2007), 217–222 Zbl1203.93086
  9. Datko R., A procedure for determination of the exponential stability of certain differential difference equations, Quart. Appl. Math. 36 (1978), 279–292 (1978) Zbl0405.34051MR0508772
  10. Wu X. J., Chaos synchronization of the new hyperchaotic Chen system via nonlinear control, Acta Phys. Sinica 22 (2006), 12, 6261–6266 

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