Numerical analysis of transient orbits by the pullback method for covariant Lyapunov vector
This work addresses the need for analyzing transient dynamics in dynamical systems, but the contribution is incremental as it adapts existing covariant Lyapunov vector methods to transient orbits.
The paper proposes a new algorithm for analyzing tangent spaces of transient orbits by pulling back vectors using covariant Lyapunov vectors, and demonstrates its application to a 3D ODE system where the vectors converge to eigenvectors at an equilibrium.
In order to analyze structure of tangent spaces of a transient orbit, we propose a new algorithm which pulls back vectors in tangent spaces along the orbit by using a calculation method of covariant Lyapunov vectors. As an example, the calculation algorithm has been applied to a transient orbit converging to an equilibrium in a three-dimensional ordinary differential equations. We obtain vectors in tangent spaces that converge to eigenvectors of the linearized system at the equilibrium. Further, we demonstrate that an appropriate perturbation calculated by the vectors can lead an orbit going in the direction of an eigenvector of the linearized system at the equilibrium.