For citation:
Kuznetsov A. P., Turukina L. V. Synchronization in systems with bimodal dynamics. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 2, pp. 35-46. DOI: 10.18500/0869-6632-2006-14-2-35-46
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 201)
Language:
Russian
Heading:
Article type:
Article
UDC:
517.9
Synchronization in systems with bimodal dynamics
Autors:
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Turukina L. V., Saratov State University
Abstract:
Considering model with bimodal dynamics we investigate the synchronization of di?erent time scales. Transition between mode-locked and mode-unlocked chaotic attractors is investigated. It is shown that this transition involves a situation in which the synchronized chaotic attractor loses its band structure.
Key words:
Reference:
- Kuramoto Y. Chemical oscillations, waves and turbulence. Berlin: Springer – Verlag; 1984. 158 p. DOI: 10.1007/978-3-642-69689-3.
- Pikovsky A, Rosenblum M, Kurths Y. Synchronization: a universal concept in nonlinear sciences. Cambridge: Cambridge University Press; 2001. 411 p.
- Mosekilde E, Maistrenko Yu, Postnov D. Chaotic synchronization: applications to living systems. Singapore: World Scientific; 2002. 440 p.
- Ott E. Chaos in dynamical systems. Cambridge: Cambridge University Press; 1993. DOI: 10.1017/CBO9780511803260.
- Anishchenko VS. Complex fluctuations in simple systems. Moscow: Nauka; 1990. (In Russian).
- Pecora LM, Carroll TL. Synchronization in chaotic systems. Phys Rev Lett. 1990;64(8):821–824. DOI: 10.1103/PhysRevLett.64.821.
- Dykman G, Landa P, Neimark Y. Synchronizing the chaotic oscillations by external force. Chaos, Solitons and Fractals. 1992;1(4):339–353. DOI: 10.1016/0960-0779(91)90025-5.
- Anishchenko VS, Vadivasova TE, Postnov DE, Safonova MA. Synchronization of chaos. Int. J. Bifurcation and Chaos. 1992;2(3):633–644. DOI: 10.1142/S0218127492000756.
- Anishchenko VS, Vadivasova TE, Postnov DE, Safonova MA. Forced and mutual synchronization of chaos. Radiotekhnika i Elektronika. 1991;36(2):338–351.
- Rulkov NF, Sushchik MM, Tsimring LS, Abarbanel HDI. Generalized synchronization of chaos in unidirectionally coupled chaotic systems. Phys. Rev. E. 1995;51(2):980–994. DOI: 10.1103/physreve.51.980.
- Rosenblum MG, Pikovsky AS, Kurths J. From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 1997;78(22):4193–4196. DOI: 10.1103/PHYSREVLETT.78.4193.
- Anishchenko VS, Silchenko AN, Khovanov IA. Synchronization of switching processes in coupled Lorenz systems. Phys. Rev. E. 1998;57(1):316–322. DOI: 10.1103/PHYSREVE.57.316.
- Landa PS, Rendel JS, Cher VF. Synchronizing oscillations in the Lorentz system. Radiophysics and Quantum Electronics. 1989;32(9):1172–1174.
- Rosenblum M, Pikovsky A, Kurths J. Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 1996;76(11):1804–1807. DOI: 10.1103/PhysRevLett.76.1804.
- Pikovsky AS, Rosenblum MG, Osipov GV, Kurths J. Phase synchronization of chaotic oscillators by external driving. Physica D. 1997;104(3-4):219–238. DOI: 10.1016/S0167-2789(96)00301-6.
- Polonsky KS, Given BD, Van Cauter E. Twenty-four-hour profiles of pulsatile patterns of insulin secretion in normal and obese subjects. J. Clin. Invest. 1988;81(2):442–448. DOI: 10.1172/JCI113339.
- Sturis J, Polonsky KS, Mosekilde E, Van Cauter E. The mechanisms underlying ultradian oscillations of insulin and glucose: A computer simulation approach. Amer. J. Physiol. 1991;260(5):E801-E809. DOI: 10.1152/ajpendo.1991.260.5.E801.
- Bergsten P, Hellman B. Glucose-induced cycles of insulin release can be resolved into distinct periods of secretory activity. Biochem Biophys Res Commun. 1993;192(3):1182–1188. DOI: 10.1006/bbrc.1993.1541.
- Barfred M, Mosekilde E, Holstein-Rathlou NH. Bifurcation analysis of nephron pressure and flow regulation. Chaos. 1996;6(3):280–287. DOI: 10.1063/1.166175.
- Holstein-Rathlou N-H, Yip K-P, Sosnovtseva OV, Mosekilde E. Synchronization phenomena in nephron interaction. Chaos. 2001;11(2):417–426. DOI: 10.1063/1.1376398.
- Sosnovtseva OV, Pavlov AN, Mosekilde E, Holstein-Rathlou N-H. Bimodal oscillations in nephron autoregulation. Phys. Rev. E. 2002;66(6):061909. DOI: 10.1103/PhysRevE.66.061909.
- Postnov DE, Shishkin AV, Sosnovtseva OV, Mosekilde E. Two-mode chaos and its synchronization properties. Phys Rev E Stat Nonlin Soft Matter Phys. 2005;72(5):056208. DOI: 10.1103/PhysRevE.72.056208.
- Ueda Y. Strange attractors and the origin of chaos. Nonlinear Science Today. 1992;2(2):1–16.
- Ueda Y, Thomsen JS, Rasmussen J, Mosekilde E. Behavior of the solution to Duffing’s equation for large forcing amplitudes. Mathematical Research. 1993;72:149.
Received:
27.12.2005
Accepted:
03.04.2006
Published:
31.05.2006
Journal issue:
Short text (in English):
(downloads: 61)
- 1845 reads