# Dynamical System Analysis for Steep Potentials

## TL;DR

This paper analyzes the dynamical behavior of steep exponential potentials using mathematical and numerical methods, revealing instability at high steepness and the absence of dark matter to dark energy transition.

## Contribution

It provides a detailed dynamical system analysis of steep exponential potentials considering various steepness indices using both theoretical and numerical approaches.

## Key findings

- Higher steepness index leads to unstable solutions
- Steep potentials do not allow phase transition from dark matter to dark energy
- Numerical and center manifold analyses corroborate the instability results

## Abstract

In this work we have performed the dynamical system analysis for steep(er) exponential potentials considering different values of the steepness index $n$. We have performed the analysis using centre manifold theory as well as by employing numerical method. We have shown that in most of the cases, the higher values of steepness index corresponds to an unstable solution. We have shown that with this steep(er) potentials one can not have a phase transition from dark matter to dark energy in the past.