Highly accurate computation of finite-time Lyapunov exponent

Abstract

Aiming at the shortcomings of current method of calculating finite-time Lyapunov exponent (FTLE), such as low accuracy, inability to obtain boundary values, etc., a method of highly accurately computing FTLE is proposed based on dual number theory. Firstly, the weakness and disadvantages of the finite difference method used widely for computing FTLE are described. Secondly, the dual number theory is introduced to evaluate the derivatives accurately and efficiently, and its distinct virtues are also presented. The computation of Cauchy-Green deformation tensors for a dynamical system is transformed into a numerical integration problem of solving the nonlinear ordinary differential equation in dual number space by the new method. Finally, the proposed method is applied to typical pendulum system and nonlinear Duffing oscillator separately. The results of simulation experiments indicate that the new method is effective, convenient and accurate for computing the field of FTLE, from which Lagrangian coherent structures can be identified successfully.