FRACTAL EROSION OF BASINS OF ATTRACTION IN COUPLED NONLINEAR-SYSTEMS

An examination is presented of how basins of attraction evolve in a coupled non-linear oscillator that has the ability to escape from a two-dimensional potential well. This work may be considered an extension of earlier studies on a single-degree-of-freedom system [1], in which it was shown that, under small parameter changes, there may exist a rapid erosion and stratification of the safe basin of attraction. Here it is shown that basin boundaries in the four-dimensional phase-space may become fractal and hence have a non-integer dimension. By analyzing cross-sections of the four-dimensional phase-space as system parameters are varied, the phenomenon of fractal basin erosion is illustrated. Such a phenomenon has important implications when assessing the global transient stability of the system.