On invariant manifolds of nonlinear discrete-time input-driven dynamical systems

Abstract

The present research work proposes a new approach to the problem of finding invariant manifolds for nonlinear discrete-time input-driven real analytic dynamical systems. The formulation of the problem is conveniently realized through a system of nonlinear first-order functional equations (NFEs) and a rather general set of necessary and sufficient conditions for solvability is derived. The solution of the aforementioned system of NFEs is proven to be a locally analytic invariant manifold that under certain conditions coincides with the stable or unstable manifold of the system, and which can be easily computed with the aid of a symbolic software package such as MAPLE. Finally, the proposed method is applied to an enzymatic bioreactor dynamics example.