# Qualitative and Numerical Analysis of a Cosmological Model Based on an Asymmetric Scalar Doublet with Minimal connections. III. Multiply-connected Factor and Character of the Singular Points

## TL;DR

This paper provides a qualitative and numerical analysis of a cosmological model with an asymmetric scalar doublet, focusing on phase space multiply-connectedness and singular point character, revealing the model's behavior near zero energy hypersurfaces.

## Contribution

It introduces the impact of multiply connected phase space factors due to nonanalytic coefficients on the model's dynamics and characterizes all singular points.

## Key findings

- Behavior near zero energy hypersurfaces identified
- Influence of multiply connected phase space discussed
- Character of all singular points revealed

## Abstract

On the basis of a qualitative and numerical analysis of a cosmological model based on an asymmetric scalar doublet of nonlinear, minimally interacting scalar fields, both classical and phantom, the behavior of the model near zero energy hypersurfaces has been revealed. The influence of the multiply connected factor of the phase space of the dynamical system, this factor being a consequence of the nonanalyticity of the coefficients of an autonomous system of differential equations, is discussed. The character of all singular points is revealed.