# Qualitative description of the universe in the interacting fluids scheme

## TL;DR

This paper qualitatively analyzes the evolution of a curved universe with interacting dark sector components modeled by Lotka-Volterra equations, revealing potential cyclic behavior and global instability due to future singularities.

## Contribution

It introduces a novel qualitative framework for universe evolution using Lotka-Volterra equations to model dark sector interactions.

## Key findings

- Presence of future singularity allows cyclic energy exchange.
- Model exhibits global instability due to singularity.
- Cyclic behavior occurs only during certain cosmic stages.

## Abstract

In this work we present a qualitative description of the evolution of a curved universe when we consider the interacting scheme for the constituents of the dark sector. The resulting dynamics can be modeled by a set of Lotka-Volterra type equations. For this model a future singularity is allowed, therefore the cyclic behavior for the energy interchange between the components of the universe is present only at some stage of the cosmic evolution. Due to the presence of the future singularity, the model exhibits global instability.