For citation:
Yanchuk S., Kapitaniak T. Riddling in the presence of small parameter mismatch. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 3, pp. 185-189. DOI: 10.18500/0869-6632-2003-11-3-185-189
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: 0)
Language:
English
Heading:
Article type:
Article
UDC:
534.015
Riddling in the presence of small parameter mismatch
Autors:
Yanchuk Serhiy, Institute of Mathematics of the National Academy of Sciences of Ukraine
Kapitaniak Tomasz, Lodz University of Technology
Abstract:
Riddling bifurcation leads to the loss of chaos synchronization in coupled identical systems. We discuss here the manifestation of the riddling bifurcation for the case of a small parameter mismaich between coupled systems. We show that for slightly nonidentical coupled systems, the transverse growth of the synchronous attractor is mediated by transverse bifurcations of unstable periodic orbits embedded into the attractor.
Key words:
Reference:
- Lai Y-C, Grebogi C, Yorke JA, Venkataramani S.C. Transitions to bubbling of chaotic systems. Phys. Rev. Lett. 1996;77(27):5361–5364. DOI: 10.1103/PhysRevLett.77.5361; Astakhov V, Shabunin А, Kapitaniak T, Anishchenko VS. Loss of chaos synchronization through the sequence of bifurcations of saddle periodic orbits. Phys. Rev. Lett. 1997;79(6):1014–1017. DOI: 10.1103/PhysRevLett.79.1014.
- Kapitaniak T, Steeb W-H. Transition to hyperchaos in coupled generalized van der Pol equations. Phys. Lett. А. 1991;152(1–2):33–36. DOI: 10.1016/0375-9601(91)90624-H; Kapitaniak Т. Transition to hyperchaos in chaotically forced coupled oscillators. Phys. Rev. Е. 1993;47(5):R2975–R2978. DOI: 10.1103/PhysRevE.47.R2975; Stefanski K. Modelling chaos and hyperchaos with 3-D maps. Chaos, Solitons and Fractals. 1998;9(1–2):83–93. DOI: 10.1016/S0960-0779(97)00051-9; Harrison MA, Lai Y-C. Route to high-dimensional chaos. Phys. Rev. Е. 1999;59(4):R3799–R3802. DOI: 10.1103/PhysRevE.59.R3799; Kapitaniak T, Maistrenko Y, Popovich S. Chaos-hyperchaos transition. Phys. Rev. Е. 2000;62(2):1972–1976. DOI: 10.1103/PhysRevE.62.1972; Yanchuk S, Kapitaniak Т. Chaos–hyperchaos transition in coupled Rössler systems. Phys. Lett. А. 2001;290(3–4):139–144. DOI: 10.1016/S0375-9601(01)00651-X.
- Johnson G, Маг D, Carroll T, Pecora L. Synchronization and imposed bifurcations in the presence of large parameter mismatch. Phys. Rev. Е. 1998;80(18):3956–3959. DOI: 10.1103/PhysRevLett.80.3956; Yanchuk S, Maistrenko Y, Lading B, Mosekilde Е. Effects of a parameter mismatch on the Synchronization of Two Coupled Chaotic oscillators. Int. J. Bifurc. Chaos. 2000;10(11):2629–2648. DOI: 10.1142/S0218127400001584.
- Yanchuk S, Kapitaniak Т. Symmetry-increasing bifurcation as a predictor of a chaos-hyperchaos transition in coupled systems. Phys. Rev. Е. 2001;64(5):056235. DOI: 10.1103/PhysRevE.64.056235.
- Astakhov V, Kapitaniak T, Shabunin А, Anishchenko V. Non-bifurcational mechanism of loss of chaos synchronization in coupled non-identical systems. Phys. Lett. А. 1999;258(2–3):99–102. DOI: 10.1016/S0375-9601(99)00291-1.
- Nagai Y, Lai Y-C. Characterization of blowout bifurcation by unstable periodic orbits. Phys. Rev. Е. 1997;55(2):R1251–R1254. DOI: 10.1103/PhysRevE.55.R1251; Nagai Y, Lai Y-C. Periodic-orbit theory of the blowout bifurcation. Phys. Rev. Е. 1997;56(4):4031–4041. DOI: 10.1103/PhysRevE.56.4031.
- Lai Y-C. Scaling laws for symmetry breaking by blowout bifurcation in chaotic systems. Phys. Rev. Е. 1997;56(2):1407–1413. DOI: 10.1103/PhysRevE.56.1407.
- Yanchuk S, Maistrenko Y, Mosekilde E. Loss of synchronization in coupled Rössler systems. Physica D. 2001;154(1–2):26–42. DOI: 10.1016/S0167-2789(01)00221-4.
- Milnor J. On the concept of attractor. Commun. Math. Phys. 1985;99(2):177–195. DOI: 10.1007/BF01212280.
Received:
08.08.2003
Accepted:
16.09.2003
Available online:
23.11.2023
Published:
31.12.2003
Journal issue:
- 181 reads