Slow manifolds for stochastic Koper models with stable L\'evy noises

TL;DR

This paper investigates the slow dynamics of a stochastic Koper model influenced by stable Le9vy noise, establishing the existence of a slow manifold and demonstrating its properties through analytical and numerical methods.

Contribution

It introduces the first analysis of slow manifolds for stochastic Koper models with stable Le9vy noise, including proof of their existence and tracking properties.

Findings

Existence of a slow manifold for the stochastic Koper model.

Verification of exponential tracking property.

Numerical simulations confirming analytical results.

Abstract

The Koper model is a vector field in which the differential equations describe the electrochemical oscillations appearing in diffusion processes. This work focuses on the understanding of the slow dynamics of stochastic Koper model perturbed by stable L\'evy noise. We establish the slow manifold for stochastic Koper model with stable L\'evy noise and verify exponential tracking property. We also present a practical example to demonstrate the analytical results with numerical simulations.