Frequency versus Lyapunov exponent map: A new approach to investigate dynamics of nonlinear magnetic systems

The complex Lyapunov exponent lambda plays a vital role in characterizing t he dynamics of a physical system. The real part of lambda has frequently be en related to as just the Lyapunov exponent and has been used for decades t o characterize the stability of the system. The imaginary part or the frequ ency of oscillations can also give valid information about the dynamics of the system, particularly how it behaves near the equilibrium points. In thi s article we will show that the frequency versus Lyapunov exponent map can give additional information about the very nature of the system and provide background for detailed analysis concerning the applicability of the contr ol technique and its robust nature. As an example of the applicability of t he map, an appropriate model to investigate the origin and growth of the au to-oscillations are the circular YIG films. Starting with the low power fer romagnetic resonance spectrum and analyzing the behavior as a function of p ower the creation and evolution of "shoots" in the map have been demonstrat ed. The resulting map gives new insights about the relationship between the underlying dynamics of the system and the "growth'' of the shoots into aut o-oscillation fingers. This approach can explain many features of the auto- oscillation behavior and gives new insights into investigating techniques t o control and synchronize chaos as well as to explain desynchronization bur sts. (C) 1998 American Institute of Physics.