# Slow manifolds for a nonlocal fast-slow stochastic evolutionary system with stable Levy noise

## TL;DR

This paper investigates the slow dynamics of a nonlocal stochastic evolutionary system influenced by Levy noise, constructing slow manifolds and demonstrating their properties through numerical examples.

## Contribution

It introduces the construction of slow manifolds for a nonlocal fast-slow stochastic system with Levy noise, including exponential tracking properties.

## Key findings

- Existence of slow manifolds for the system.
- Demonstration of exponential tracking property.
- Numerical simulations illustrating theoretical results.

## Abstract

This work aims at understanding the slow dynamics of a nonlocal fast-slow stochastic evolutionary system with stable Levy noise. Slow manifolds along with exponential tracking property for a nonlocal fast-slow stochastic evolutionary system with stable Levy noise are constructed and two examples with numerical simulations are presented to illustrate the results.