ASYMMETRICAL COUPLING INFLUENCE ON BIFURCATIONAL MECHANIZMS OF ANTIPHASE CHAOTIC SYNCHRONIZATION DESTRUCTION

Cite this article as:

Astakhov V. V., Shabunin А. V., Stalmakhov P. . ASYMMETRICAL COUPLING INFLUENCE ON BIFURCATIONAL MECHANIZMS OF ANTIPHASE CHAOTIC SYNCHRONIZATION DESTRUCTION. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 2, pp. 40-54. DOI: https://doi.org/10.18500/0869-6632-2007-15-2-40-54

The work is devoted to anti-phase controlled synchronization of chaos in diffusivelly coupled cubic maps. Influence of asymmetry of controlling feed-back coupling on mechanizms of the synchronization loss is considered. A new bifurcational scenarium which includes a sequence of transcritical and saddle-repeller bifurcation has been found. We demonstrate that the same squence of bifurcations can lead to either «bubbling» or «riddling» transitions in dependance of assymetry value.

 

Authors: 
Astakhov V. V., Yuri Gagarin State Technical University of Saratov, ul. Politechnicheskaya, 77, Saratov, 410054, Russia , v-astakhov@yandex.ru
Shabunin А. V., Saratov State University, ul. Astrakhanskaya, 83, Saratov, 410012, Russia , shabuninav@info.sgu.ru
Stalmakhov P. А., Saratov State University, ul. Astrakhanskaya, 83, Saratov, 410012, Russia ,
Key words: 
-
DOI: 
10.18500/0869-6632-2007-15-2-40-54
Literature

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3. Astakhov V., Shabunin A., Kapitaniak T., Anishchenko V. Loss of chaos synchronization through the sequence of bifurcations of saddle periodic orbits // Phys. Rev. Lett. 1997. Vol. 79. P. 1014.

4. Astakhov V., Hasler M., Kapitaniak T., Shabunin A.,Anishchenko V. Effect of parameter mismatch on the mechanism of chaos synchronization loss in coupled systems // Phys. Rev. E. 1998. Vol. 58. P. 5620.

5. Platt N., Spiegel E.A., Tresser C. On-off intermittency: A mechanism for bursting // Phys. Rev. Lett. 1993. Vol. 70. P. 279.

6. Lai Y.-C., Grebogi C., Yorke J.A., Venkataramani S.C. Riddling bifurcation in chaotic dynamical systems // Phys. Rev. Lett. 1996. Vol. 77. P. 1.

Heading: 
Deterministic Chaos
Status: 
одобрено к публикации
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BibTeX

@article{Астахов -IzvVUZ_AND-15-2-40,
author = {V. V. Astakhov and А. V. Shabunin and P. А. Stalmakhov},
title = {ASYMMETRICAL COUPLING INFLUENCE ON BIFURCATIONAL MECHANIZMS OF ANTIPHASE CHAOTIC SYNCHRONIZATION DESTRUCTION},
year = {2007},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {15},number = {2},
url = {https://old-andjournal.sgu.ru/en/articles/asymmetrical-coupling-influence-on-bifurcational-mechanizms-of-antiphase-chaotic},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2007-15-2-40-54},pages = {40--54},issn = {0869-6632},
keywords = {-},
abstract = {The work is devoted to anti-phase controlled synchronization of chaos in diffusivelly coupled cubic maps. Influence of asymmetry of controlling feed-back coupling on mechanizms of the synchronization loss is considered. A new bifurcational scenarium which includes a sequence of transcritical and saddle-repeller bifurcation has been found. We demonstrate that the same squence of bifurcations can lead to either «bubbling» or «riddling» transitions in dependance of assymetry value.   }}