zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Bifurcation continuation, chaos and chaos control in nonlinear Bloch system. (English) Zbl 1221.78013
Summary: A detailed analysis is undertaken to explore the stability and bifurcation pattern of the nonlinear Bloch equation known to govern the dynamics of an ensemble of spins, controlling the basic process of nuclear magnetic resonance. After the initial analysis of the parameter space and stability region identification, we utilize the MATCONT package to analyze the detailed bifurcation scenario as the two important physical parameters γ (the normalized gain) and c (the phase of the feedback field) are varied. A variety of patterns are revealed not studied ever before. Next we explore the structure of the chaotic attractor and how the identification of unstable periodic orbit (UPO) can be utilized to control the onset of chaos.
78A25General electromagnetic theory
37D45Strange attractors, chaotic dynamics
37G15Bifurcations of limit cycles and periodic orbits
37N20Dynamical systems in other branches of physics
[1]Deville, G.; Bernier, M.; Delrieux, J. M.: NMR multiple echoes observed in solid 3He, Phys rev B 19, 5666-5688 (1979)
[2]Bowtell, R.; Bowley, R. M.; Glover, P.: Multiple spin echoes in liquids in a high magnetic field, J mag reson 88, 643-651 (1990)
[3]He, Q.; Richter, W.; Vathyam, S.; Warren, W. S.: Intermolecular multiple-quantum coherences and cross correlations in solution nuclear magnetic resonance, J chem phys 98, 6779-6800 (1993)
[4]Jeener, J.; Vlassenbroek, A.; Broakaert, P.: Unified derivation of the dipolar field and relaxation terms in the Bloch – Redfield equations of liquid NMR, J chem phys 103, 1309-1332 (1995)
[5]Jeener, J.: Dynamical effects of the dipolar field inhomogeneities in high-resolution NMR: spectral clustering and instabilities, Phys rev lett 82, 1772-1775 (1999)
[6]Abergel, D.; Louis-Joseph, A.; Lallemand, J. -Y.: Self-sustained maser oscillations of a large magnetization driven by a radiation damping-based electronic feedback, J chem phys 116, 7073-7080 (2002)
[7]Dhooge, A.; Govaerts, W.; Kuznetsov, Y. A.: MATCONT: A Matlab package for numerical bifurcation analysis of odes, ACM trans math software 29, 141-164 (2003) · Zbl 1070.65574 · doi:10.1145/779359.779362
[8]Mestrom W. Continuation of limit cycles in MATLAB, Master thesis, Mathematical Institute, Utrecht University, The Netherlands, 2002.
[9]Riet A. A continuation toolbox in MATLAB, Master thesis, Mathematical Institute, Utrecht University, The Netherlands, 2000.
[10]Ott, E.; Grebogi, C.; Yorke, J. A.: Controlling chaos, Phys rev lett 64, 1196-1199 (1990) · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196
[11]Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems, Phys rev lett 64, 821-824 (1990)
[12]Pikovsky, A.; Rosenblum, M.; Kurths, J.: In synchronization: a universal concept in nonlinear science, (2001)
[13]Boccaletti, S.; Kurths, J.; Osipov, G.; Valladares, D. L.; Zhou, C. S.: The synchronization of chaotic systems, Phys rep 366, 1-101 (2002) · Zbl 0995.37022 · doi:10.1016/S0370-1573(02)00137-0
[14]Pyragas, K.: Continuous control of chaos by self-controlling feedback, Phys lett A 170, 421-428 (1992)
[15]Jackson, E. A.; Grosu, I.: An open-plus-closed-loop (OPCL) control of complex dynamic systems, Physica D 85, 1-9 (1995) · Zbl 0888.93034 · doi:10.1016/0167-2789(95)00171-Y
[16]Yu, H. J.; Liu, Y. Z.; Peng, J. H.: Continuous control based on stability criterion, Phys rev E 69, 066203-066211 (2004)
[17]Hunt, E. R.: Dynamical control of a chaotic laser: experimental stabilization of a globally coupled system, Phys rev lett 68, 1259-1262 (1992)
[18]Hobson, R. F.; Kayser, R. J.: Mag reson, Mag reson 20, 458 (1975)
[19]Abergel, D.: Chaotic solutions of the feedback driven Bloch equations, Phys lett A 302, 17-22 (2002) · Zbl 0997.82045 · doi:10.1016/S0375-9601(02)01079-4
[20]Uçar, A.; Lonngren, K. E.; Bai, E. W.: Synchronization of chaotic behavior in nonlinear Bloch equations, Phys lett A 314, 96-101 (2003) · Zbl 1035.34037 · doi:10.1016/S0375-9601(03)00864-8
[21]Guckenheimer, J. A.; Holmes, P.: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, (1983)
[22]Shinbrot, T.; Grebogi, C.; Ott, E.; Yorke, J. A.: Using small perturbations to control chaos, Nature (London) 363, 411-417 (1993)