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Balmforth, N. J.; Craster, R. V.

Synchronizing Moore and Spiegel. (English) Zbl 0938.37018

Chaos 7, No. 4, 738-752 (1997).
Summary: This paper presents a study of bifurcations and synchronization, in the sense of L. M. Pecora and T. L. Carroll [Phys. Rev. Lett. 64, 821-824 (1990; Zbl 0938.37018)] in the Moore-Spiegel oscillator equations. Complicated patterns of period-doubling, saddle-node, and homoclinic bifurcations are found and analyzed. Synchronization is demonstrated by numerical experiment, periodic orbit expansion, and by using coordinate transformations. Synchronization via the resetting of a coordinate after a fixed interval is also successful in some cases. The Moore-Spiegel system is one of a general class of dynamical systems and synchronization is considered in this more general context.

Cited in 2 Reviews
Cited in 5 Documents

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C29 Homoclinic and heteroclinic orbits for dynamical systems
37C45 Dimension theory of smooth dynamical systems
94C05 Analytic circuit theory
37N35 Dynamical systems in control

Keywords:

complicated patterns; period-doubling; saddle-node; homoclinic bifurcations; synchronization; periodic orbit expansion; Moore-Spiegel oscillator; oscillator

Citations:

Zbl 0938.37018
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Full Text: DOI Link

References:

[1] DOI: 10.1103/PhysRevA.44.2374 · doi:10.1103/PhysRevA.44.2374
[2] Tresser C., Chaos 5 pp 693– (1995) · Zbl 1055.34506 · doi:10.1063/1.166101
[3] He R., Phys. Rev. A 46 pp 7387– (1994) · doi:10.1103/PhysRevA.46.7387
[4] DOI: 10.1086/148562 · doi:10.1086/148562
[5] Baker N. H., Q. J. Mech. Appl. Math. 24 pp 391– (1971) · Zbl 0226.70018 · doi:10.1093/qjmam/24.4.391
[6] Marzec C. J., SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 38 pp 403– (1980) · Zbl 0471.65052 · doi:10.1137/0138034
[7] DOI: 10.1103/PhysRevLett.74.5028 · doi:10.1103/PhysRevLett.74.5028
[8] Artuso R., Nonlinearity 3 pp 325– (1990) · Zbl 0702.58064 · doi:10.1088/0951-7715/3/2/005
[9] Cvitanovic P., Physica D 3 pp 109– (1995) · Zbl 1194.37051 · doi:10.1016/0167-2789(94)00256-P
[10] Cvitanovic P., Nonlinearity 6 pp 277– (1993) · Zbl 0773.58013 · doi:10.1088/0951-7715/6/2/008
[11] DOI: 10.1103/PhysRevLett.76.904 · doi:10.1103/PhysRevLett.76.904
[12] DOI: 10.1103/PhysRevE.51.980 · doi:10.1103/PhysRevE.51.980
[13] DOI: 10.1103/PhysRevE.47.3889 · doi:10.1103/PhysRevE.47.3889
[14] Brown R., Chaos 7 pp 395– (1997) · Zbl 0933.37026 · doi:10.1063/1.166213
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