This paper is a concept paper about a suggestion proposed by Nathan Forrester, in the last year conference to extend eigenvalue analysis to nonlinear models. His idea was to consider higher order terms of the Taylor series expansion when approximating nonlinear models. In this paper, we demonstrate the feasibility of Nathan's idea. The main contribution of this paper is to devise a pragmatic approach to solve the resulting equations of Taylor series expansion. This pragmatic approach is based on our novel concept of 'smoothed Jacobian' matrix, which is computed from both the ordinary Jacobian matrix and the set of Hessian matrices. Recall that the elements of the ordinary Jacobian matrix represent slopes of relationships, while the elements of the Hessian matrices represent curvatures of relationships. So by integrating the elements the ordinary Jacobian with the elements of the Hessian matrices, we are actually smoothing the slopes given the knowledge about curvatures.  Consequently we are smoothing the time trajectories of eigenvalues and eigenvectors in nonlinear models.