# Dynamical Systems Analysis of K-essence Model

## TL;DR

This paper analyzes the stability of k-essence cosmological models with quadratic kinetic terms, showing they tend to evolve towards stable quintessence solutions with canonical dark energy.

## Contribution

It provides a dynamical systems analysis of k-essence models with quadratic kinetic terms, revealing their tendency to evolve into stable quintessence solutions.

## Key findings

- Models with quadratic kinetic terms are dynamically stable.
- Cosmologically consistent models evolve towards quintessence.
- Stable solutions correspond to canonical dark energy.

## Abstract

In the present work we investigate the stability of the k-essence models allowing upto quadratic terms of the kinetic energy. The system of field equations is written as an autonomous system in terms of dimensionless variables and the stability criteria of the equilibria have been extensively investigated. The results strongly indicate that cosmologically consistent models dynamically evolve towards the quintessence model, a stable solution with a canonical form of the dark energy.