Dynamical properties of laser models based on the Maxwell Bloch equation are studied. Instances of stability and chaotic behavior are investigated. Special solutions of the system one of which reduces to the Lotka Volterra system under simplifying assumptions are derived. Reasons for the absence of oscillating solutions in the modified systems are studied.

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High field magnetic resonance offers new opportunities because of its high SNR and better spectral resolution for MRI and MRS. However, new problems also emerge at high field. As the field strength increases, the wavelength in the tissue becomes shorter and comparable with the body dimensions. This perturbs the field and also causes standing waves within the patient as a result of the impedance mismatching at the tissue interfaces. Due to the complexity of the boundary conditions and the solution of Maxwell's equations, an exact analytical calculation for a loaded RF resonator has not been possible. In this paper, we present a birdcage coil simulation study based on a 3D finite element method (FEM) model for the characterization of the field within the tissue. First, the accuracy of the FEM solutions is validated by the 2D analytical solutions at 64 and 223 MHz. In these solutions, the frequency dependence of the conductivity and permittivity is also taken into account. Then, a more realistic 3D model is studied. The results are compared with the experimental measurements. It is shown that the 3D model makes it possible to explore the effects of the end rings in the presence of a tissue sample inside the coil.