Nonlinear resonances and transitions to chaotic dynamics of a driven magnetic moment

Abstract We examine a magnetic moment subject to a static external magnetic field and a time dependent driving magnetic field. Taking the system in the highly anisotropic limit, like that of a thin film, we lower the complexity of the system so that it may be analyzed for transitions to chaos analytically using the Melnikov method. Guided by the calculation of the Melnikov bifurcation functions we computationally calculated the Lyapunov characteristic exponents for several lines in parameter space and find that the Melnikov method is a good predictor of chaotic motion for sufficiently small external fields. Motion plots and Poincare sections are also plotted for several parameter space points to observe the transitions to and from chaos around the calculated Melnikov bifurcations functions.