| Title:
|
Analysis of an on-off intermittency system with adjustable state levels (English) |
| Author:
|
Cang, Shi-Jian |
| Author:
|
Chen, Zeng-Qiang |
| Author:
|
Yuan, Zhu-Zhi |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
455-468 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
on-off intermittency |
| Keyword:
|
multi-state |
| Keyword:
|
invariant subspace |
| Keyword:
|
control analysis |
| Keyword:
|
statistical analysis |
| MSC:
|
37C70 |
| MSC:
|
37D45 |
| MSC:
|
37N35 |
| MSC:
|
62J09 |
| MSC:
|
62J10 |
| MSC:
|
62J99 |
| MSC:
|
62M15 |
| MSC:
|
93C10 |
| idZBL:
|
Zbl 1177.37028 |
| idMR:
|
MR2459064 |
| . |
| Date available:
|
2009-09-24T20:36:37Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135865 |
| . |
| Reference:
|
[1] Ashwin P., Buescu, J., Stewart I.: From attractor to chaotic saddle: A tale of transverse instability.Nonlinearity 9 (1996), 703–737 Zbl 0887.58034, MR 1393154 |
| Reference:
|
[2] Bojowald M., Kastrup H. A.: Symmetry reduction for quantized diffeomorphism invariant theories of connections.Class. Quantum. Grav. 17 (2000), 3009–3043 Zbl 0977.83019, MR 1777001 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[8] Heagy J. F., Platt, N., Hammel S. M.: Characterization of on-off intermittency.Phys. Rev. E 49 (1994), 1140–1150 |
| Reference:
|
[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 |
| Reference:
|
[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 MR 2288582 |
| Reference:
|
[11] Kapitaniak T., Lai Y. C., Grebogi C.: Blowout bifurcation of chaotic saddles.Discrete Dynamics in Nature and Society 3 (1999), 9–13 Zbl 0982.37018 |
| Reference:
|
[12] Kapitaniak T., Maistrenko Y.: Riddling bifurcations in coupled piecewise linear maps.Physica D 126 (1999), 18–26 Zbl 0964.37031, MR 1676692 |
| Reference:
|
[13] Korn H., Faure P.: Is there chaos in brain? II.Experimental evidence and related models. Biologies 326 (2003), 787–840 |
| Reference:
|
[14] Ott E., Sommerer J. C.: Blowout bifurcations: The occurrence of riddled basins and on-off intermittency.Phys. Lett. A 188 (1994), 39–47 |
| Reference:
|
[15] Platt N., Hammel S. M., Heagy J. F.: Effects of additive noise on on-off intermittency.Phys. Rev. Lett. 72 (1994), 3498–3501 |
| Reference:
|
[16] Platt N., Spiegel E. A., Tresser C.: On-off intermittency: a mechanism for bursting.Phys. Rev. Lett. 70 (1993), 279–282 |
| . |
