, Volume 5, Issue 1, pp 153-169

Multiple time scales for nonlinear systems

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Abstract

In this paper we extend the results on the multiple time-scale structure for linear autonomous systems of the form $$\dot x = A( \in )x$$ (cf. Coderchet al. [1]) to nonlinear autonomous systems. Our main result is in obtaining conditions under which the linearized system and the nonlinear system around an equilibrium point have the same time-scale structure.

This research was supported in part by NASA under grant NAG 2-243.
All eigenvalues ofA 0 (ε) are in the open left half plane except possibly some at the origin. Further, there are no generalized eigenvectors associated with the zero eigenvalue.