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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 $\gamma$ (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.
MSC:
 78A25 General electromagnetic theory 37D45 Strange attractors, chaotic dynamics 37G15 Bifurcations of limit cycles and periodic orbits 37N20 Dynamical systems in other branches of physics
MATCONT