# Computational singular perturbation method for nonstandard slow-fast systems

## TL;DR

This paper extends the computational singular perturbation (CSP) method to nonstandard slow-fast systems with normally hyperbolic attracting critical manifolds, providing new formulas and demonstrating its applicability on complex examples.

## Contribution

It adapts the CSP method to nonstandard systems, offering new formulas and the first concrete demonstrations on genuinely nonstandard examples.

## Key findings

- Successfully extended CSP to nonstandard systems
- Derived new formulas for the adapted CSP method
- Demonstrated applicability on complex nonstandard examples

## Abstract

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, 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 {\it 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.