Analysis of an on-off intermittency system with adjustable state levels

Shi-Jian Cang; Zeng-Qiang Chen; Zhu Zhi Yuan

Kybernetika (2008)

  • Volume: 44, Issue: 4, page 455-468
  • ISSN: 0023-5954

Abstract

top
We consider a chaotic system with a double-scroll attractor proposed by Elwakil, composing with a second-order system, which has low-dimensional multiple invariant subspaces and multi-level on-off intermittency. This type of composite system always includes a skew-product structure and some invariant subspaces, which are associated with different levels of laminar phase. In order for the level of laminar phase be adjustable, we adopt a nonlinear function with saturation characteristic to tune the range of a certain state variable so that the number and position of the laminar phase level can be arbitrarily controlled. We find that there exist many interesting statistical characteristics in this complex system, such as the probability distribution of the laminar lengths with -3/2 exponent in the power law and random jumping of the system trajectories.

How to cite

top

Cang, Shi-Jian, Chen, Zeng-Qiang, and Yuan, Zhu Zhi. "Analysis of an on-off intermittency system with adjustable state levels." Kybernetika 44.4 (2008): 455-468. <http://eudml.org/doc/33941>.

@article{Cang2008,
abstract = {We consider a chaotic system with a double-scroll attractor proposed by Elwakil, composing with a second-order system, which has low-dimensional multiple invariant subspaces and multi-level on-off intermittency. This type of composite system always includes a skew-product structure and some invariant subspaces, which are associated with different levels of laminar phase. In order for the level of laminar phase be adjustable, we adopt a nonlinear function with saturation characteristic to tune the range of a certain state variable so that the number and position of the laminar phase level can be arbitrarily controlled. We find that there exist many interesting statistical characteristics in this complex system, such as the probability distribution of the laminar lengths with -3/2 exponent in the power law and random jumping of the system trajectories.},
author = {Cang, Shi-Jian, Chen, Zeng-Qiang, Yuan, Zhu Zhi},
journal = {Kybernetika},
keywords = {on-off intermittency; multi-state; invariant subspace; control analysis; statistical analysis; on-off intermittency; multi-state; invariant subspace; control analysis; statistical analysis},
language = {eng},
number = {4},
pages = {455-468},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Analysis of an on-off intermittency system with adjustable state levels},
url = {http://eudml.org/doc/33941},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Cang, Shi-Jian
AU - Chen, Zeng-Qiang
AU - Yuan, Zhu Zhi
TI - Analysis of an on-off intermittency system with adjustable state levels
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 4
SP - 455
EP - 468
AB - We consider a chaotic system with a double-scroll attractor proposed by Elwakil, composing with a second-order system, which has low-dimensional multiple invariant subspaces and multi-level on-off intermittency. This type of composite system always includes a skew-product structure and some invariant subspaces, which are associated with different levels of laminar phase. In order for the level of laminar phase be adjustable, we adopt a nonlinear function with saturation characteristic to tune the range of a certain state variable so that the number and position of the laminar phase level can be arbitrarily controlled. We find that there exist many interesting statistical characteristics in this complex system, such as the probability distribution of the laminar lengths with -3/2 exponent in the power law and random jumping of the system trajectories.
LA - eng
KW - on-off intermittency; multi-state; invariant subspace; control analysis; statistical analysis; on-off intermittency; multi-state; invariant subspace; control analysis; statistical analysis
UR - http://eudml.org/doc/33941
ER -

References

top
  1. Ashwin P., Buescu, J., Stewart I., From attractor to chaotic saddle: A tale of transverse instability, Nonlinearity 9 (1996), 703–737 (1996) Zbl0887.58034MR1393154
  2. Bojowald M., Kastrup H. A., Symmetry reduction for quantized diffeomorphism invariant theories of connections, Class. Quantum. Grav. 17 (2000), 3009–3043 Zbl0977.83019MR1777001
  3. Covas E., Tavakol R., Ashwin P., Tworkowski, A., Brooke J. M., In-out intermittency in PDE and ODE models of axisymmetric mean field dynamos, Chaos 11 (2001), 404–409 
  4. Elwakil A. S., Salama K. N., Kennedy M. P., A system for chaos generation and its implementation in monolithic form, Proc. IEEE Internat. Symposium on Circuits and Systems 5 (2000), 217–220 
  5. Faure P., Korn H., Is there chaos in the brain? I, Concepts of nonlinear dynamics and methods of investigation. Life Sciences 324 (2001), 773–793 
  6. Feng D. L., Yu C. X., Xie J. L., Ding W. X., On-off intermittencies in gas discharge plasma, Phys. Rev. E 58 (1998), 3678–3685 (1998) 
  7. Feng D. L., Zheng J., Huang W., Yu C. X., Ding W. X., Type-I-like intermittent chaos in multicomponent plasmas with negative ions, Phys. Rev. E 54 (1996), 2839–2843 (1996) 
  8. Heagy J. F., Platt, N., Hammel S. M., Characterization of on-off intermittency, Phys. Rev. E 49 (1994), 1140–1150 (1994) 
  9. John T., Stannarius, R., Behn U., On-off intermittency in stochastically driven electro-hydrodynamic convection in nematics, Phys. Rev. Lett. 83 (1999), 749–752 (1999) 
  10. Kapitaniak T., Blowout bifurcation and on-off intermittency in pulse neural networks with multiple modules, International Journal of Bifurcation and Chaos 16 (2006), 3309–3321 MR2288582
  11. Kapitaniak T., Lai Y. C., Grebogi C., Blowout bifurcation of chaotic saddles, Discrete Dynamics in Nature and Society 3 (1999), 9–13 (1999) Zbl0982.37018
  12. Kapitaniak T., Maistrenko Y., Riddling bifurcations in coupled piecewise linear maps, Physica D 126 (1999), 18–26 (1999) Zbl0964.37031MR1676692
  13. Korn H., Faure P., Is there chaos in brain? II, Experimental evidence and related models. Biologies 326 (2003), 787–840 
  14. Ott E., Sommerer J. C., Blowout bifurcations: The occurrence of riddled basins and on-off intermittency, Phys. Lett. A 188 (1994), 39–47 (1994) 
  15. Platt N., Hammel S. M., Heagy J. F., Effects of additive noise on on-off intermittency, Phys. Rev. Lett. 72 (1994), 3498–3501 (1994) 
  16. Platt N., Spiegel E. A., Tresser C., On-off intermittency: a mechanism for bursting, Phys. Rev. Lett. 70 (1993), 279–282 (1993) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.