An innovative approach for identifying boundaries of a basin of attraction for a dynamical system using Monte Carlo techniques and Lyapunov exponents

Stability analysis of nonlinear dynamical systems involves identifying the basins of attraction (BoA) of attractors which is a challenging task. The research on this topic can be categorized into three groups: Non-Lyapunov-based, Lyapunov-function-based, and Lyapunov-exponents-based methods. Non-Lyapunov-based methods have low computational load, but their predictability is low. Lyapunov-function-based methods have strong mathematical background, but not only are not exclusive about the BoA, but also are not feasible for most of the real world applications. Lyapunov-exponents-based methods are capable of performing the task for highly complex systems. However, their computational load is high. In this paper a novel approach is introduced which employs Lyapunov exponents, to benefit from its advantages, and Monte Carlo techniques to reduce the load of computations. The method is demonstrated by two illustrative examples.