# Effects of Limiting Memory Capacity on the Behaviour of Exemplar Dynamics

## TL;DR

This paper investigates how limiting memory capacity in exemplar models influences language change, showing that while extinction of categories is inevitable, the rate of extinction varies with memory limits.

## Contribution

It introduces a simplified exemplar model to analyze the impact of memory constraints on language category extinction, a question not previously addressed.

## Key findings

- All but one sound category eventually become extinct.
- Memory limits affect the speed of category extinction.
- Extinction occurs regardless of memory capacity constraints.

## Abstract

Exemplar models are a popular class of models used to describe language change. Here we study how limiting the memory capacity of an individual in these models affects the system's behaviour. In particular we demonstrate the effect this change has on the extinction of categories. Previous work in exemplar dynamics has not addressed this question. In order to investigate this, we will inspect a simplified exemplar model. We will prove for the simplified model that all the sound categories but one will always become extinct, whether memory storage is limited or not. However, computer simulations show that changing the number of stored memories alters how fast categories become extinct.