Oscillation types, multistability, and basins of attractors in symmetrically coupled period-doubling systems

Chaos, Solitons and Fractals

Volumn 15, Issue 4, 2003, Pages 695-711

  Bezruchko, B P ^a   Prokhorov, M D ^a   Seleznev, Ye P ^a  

^a INSTITUTE OF RADIO ENGINEERING AND ELECTRONICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; OSCILLATIONS; RESONATORS; SYNCHRONIZATION;

PERIOD-DOUBLING SYSTEMS;

NONLINEAR SYSTEMS;

EID: 0037289963     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(02)00171-6     Document Type: Article

References (38)

1. Frøyland J. Some symmetric, two-dimensional, dissipative maps. Physica D. 8:1983;423-434.
2. Kaneko K. Similarity structure and scaling property of the period-adding phenomena. Prog. Theor. Phys. 69:1983;403.
3. Yuan J.-M., Tung M., Feng D.H., Narducci L.M. Instability and irregular behavior of coupled logistic equations. Phys. Rev. A. 28:1983;1662.
4. Buskirk R., Jeffries C. Observation of chaotic dynamics of coupled nonlinear oscillators. Phys. Rev. A. 31:1985;3332-3357.
5. Sakaguchi H., Tomita K. Bifurcations of the coupled logistic map. Prog. Theor. Phys. 78:1987;305-315.
6. Satoh K. Quasiperiodic route to chaos in a coupled logistic map. J. Phys. Soc. Jpn. 60:1991;718-719.
7. Reick C., Mosekilde E. Emergence of quasiperiodicity in symmetrically coupled, identical period-doubling systems. Phys. Rev. E. 52:1995;1418-1435.
8. Kuznetsov S.P. Universality and similarity in the behavior of coupled Feigenbaum systems. Izv. Vyssh. Uchebn. Zaved. Radiofiz. 28:1985;991-1007.
9. Satoh K., Aihara T. Self-similar structures in the phase diagram of a coupled-logistic map. J. Phys. Soc. Jpn. 59:1990;1123-1126.
10. Kook H., Ling F.H., Schmidt G. Universal behavior of coupled nonlinear systems. Phys. Rev. A. 43:1991;2700-2708.
11. Kim S.-Y. Universal scaling in coupled maps. Phys. Rev. E. 52:1995;1206-1209.
12. Ferretti A., Rahman N.K. Coupled logistic maps in physico-chemical processes: coexisting attractors and their applications. Chem. Phys. Lett. 140:1987;71-75.
13. Astakhov V.V., Bezruchko B.P., Gulyaev Yu.V., Seleznev Ye.P. Multistable states of dissipatively coupled Feigenbaum systems. Pis'ma Zh. Tekh. Fiz. 15:1989;60-65.
14. Astakhov V.V., Bezruchko B.P., Erastova E.N., Seleznev Ye.P. Types of oscillation and their evolution in dissipatively coupled Feigenbaum systems. Zh. Tekh. Fiz. 60:1990;19-26.
15. Astakhov V.V., Bezruchko B.P., Pudovochkin O.B., Seleznev Ye.P. Phase multistability and transition to oscillation steady in nonlinear systems with period-doubling. Radiotekh. Elektron. (Moscow). 38:1993;291-295.
16. Prokhorov M.D. Oscillation types of dissipatively coupled period-doubling systems at strong coupling. Izv. Vyssh. Uchebn. Zaved. Prikl. Nelin. Dinam. 4:1996;99-107.
17. Carvalho R., Fernandez B., Mendes R.V. From synchronization to multistability in two coupled quadratic maps. Phys. Lett. A. 285:2001;327-338.
18. Gu Y., Tung M., Yuan J.M., Feng D.H., Narducci L.M. Crises and hysteresis in coupled logistic maps. Phys. Rev. Lett. 52:1984;701-704.
19. Metzler W., Beau W., Frees W., Ueberla A. Symmetry and self-similarity with coupled logistic maps. Z. Naturforsch. A. 42:1987;310-318.
20. Inoue M., Nishi Y. Highly complicated basins of periodic attractors in coupled chaotic maps. Prog. Theor. Phys. 95:1996;685-690.
21. Bezruchko B.P., Seleznev Ye.P. Basins of attraction for chaotic attractors in coupled systems with period-doubling. Pis'ma Zh. Tekh. Fiz. 23:1997;40-46.
22. Anishchenko V.S. Dynamical chaos in physical systems. 1989;Teubner, Leipzig.
23. Gyllenberg M., Soderbacka G., Ericsson S. Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model. Math. Biosci. 118:1992;25.
24. Bezruchko B.P., Prokhorov M.D., Seleznev Ye.P. Features of the parameter space structure for a system of two coupled nonautonomous nonisochronous oscillators. Pis'ma Zh. Tekh. Fiz. 22:1996;61-66.
25. Yamada T., Fujisaka H. Stability theory of synchronized motion in coupled-oscillator systems. II. The mapping approach. Prog. Theor. Phys. 70:1983;1240.
26. Pikovsky A.S. On the interaction of strange attractors. Z. Phys. B. 55:1984;149-154.
27. Kuznetsov S.P., Pikovsky A.S. Symmetry breaking bifurcation in the system of dissipatively coupled recurrent mappings. Izv. Vyssh. Uchebn. Zaved. Radiofiz. 32:1989;49-54.
28. Pikovsky A.S., Grassberger P. Symmetry breaking bifurcation for coupled chaotic attractors. J. Phys. A. 24:1991;4587-4597.
29. Astakhov V., Shabunin A., Kapitaniak T., Anishchenko V. Loss of chaos synchronization through the sequence of bifurcations of saddle periodic orbits. Phys. Rev. Lett. 79:1997;1014-1017.
30. Kapitaniak T., Maistrenko Y.L. Chaos synchronization and riddled basins in two coupled one-dimensional maps. Chaos, Solitons & Fractals. 9:1998;271-282.
31. Yang H.L., Pikovsky A.S. Riddling, bubbling, and Hopf bifurcation in coupled map systems. Phys. Rev. E. 60:1999;5474-5478.
32. Maistrenko Yu.L., Maistrenko V.L., Popovich A., Mosekilde E. Transverse instability and riddled basins in a system of two coupled logistic maps. Phys. Rev. E. 57:1998;2713-2724.
33. Maistrenko Yu.L, Maistrenko V.L., Popovych O., Mosekilde E. Desynchronization of chaos in coupled logistic maps. Phys. Rev. E. 60:1999;2817-2830.
34. Popovych O., Maistrenko Yu., Mosekilde E., Pikovsky A., Kurths J. Transcritical riddling in a system of coupled maps. Phys. Rev. E. 63:2001;036201.
35. Udwadia F.E., Raju N. Some global properties of a pair of coupled maps: quasi-symmetry, periosynchronicity synchronicity. Physica D. 111:1998;16-26.
36. Mira C., Fournier-Prunaret D., Gardini L., Kawakami H., Cathala J.C. Basin bifurcations of two-dimensional noninvertible maps: fractalization of basins. Int. J. Bif. Chaos. 4:1995;343-381.
37. Astakhov V.V., Bezruchko B.P., Kuznetsov S.P., Seleznev Ye.P. Features of quasiperiodic motion occurrence in a system of dissipatively coupled periodically driven nonlinear oscillators. Pis'ma Zh. Tekh. Fiz. 14:1988;37-41.
38. Astakhov V.V., Bezruchko B.P., Ponomarenko V.I., Seleznev Ye.P. Multistability in a system of radiotechnical oscillators with capacitive coupling. Radiotekh. Elektron. (Moscow). 36:1991;2167-2170.