What Happens When an Equilibrium Becomes Unstable? An Introduction to Linear Stability Analysis

Abstract

The microscopic concept of “statistical averaging” allows us to describe the complicated behaviour of all the atoms and molecules in a chemical reaction by the macroscopic concept of the rate equation. We can examine our reaction on a higher level and do not have to pay attention to what is going on on the lower one. However there is a “gray” area between these two levels since the microscopic processes permanently produce small perturbations of the macroscopic levels.
If an equilibrium state is perturbed, the perturbation can damp out and we have a stable state, or it can increase and create a new stable state. Below, we discuss in detail what can happen when an equilibrium state experiences small perturbations.