Computational Singular Perturbation Method for Nonstandard Slow-Fast Systems

The computational singular perturbation (CSP) method is an algorithm which iteratively approximates slow manifolds and fast fibers in multiple-timescale dynamical systems. Since its inception due to Lam and Goussis [Twenty-Second Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, 1989, pp. 931-941], the convergence of the CSP method has been explored in depth; however, rigorous applications have been confined to the standard framework, where the separation between slow and fast variables is made explicit in the dynamical system. This paper adapts the CSP method to nonstandard slow-fast systems having a normally hyperbolic attracting critical manifold. We give new formulas for the CSP method in this more general context, and provide the first concrete demonstrations of the method on genuinely nonstandard examples.