# Qualitative and Numerical Analysis of a Cosmological Model Based on an Asymmetric Scalar Doublet with Minimal connections. IV. Numerical Modeling and Types of Behavior of the Model

## TL;DR

This paper conducts a qualitative and numerical study of a cosmological model with an asymmetric scalar doublet, revealing behaviors near zero energy hypersurfaces, including limit cycles and tendencies toward Euclidean space.

## Contribution

It provides the first detailed numerical modeling of a scalar doublet cosmological model, identifying behaviors like limit cycles and the influence of initial conditions and constants.

## Key findings

- Existence of limit cycles on zero-energy hypersurfaces.
- Three distinct behavioral types based on parameters.
- Models tend to approach 4D Euclidean space hypersurfaces.

## 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 -- one classical and one phantom, peculiarities of the behavior of the model near zero energy hypersurfaces have been revealed. Numerical models have been constructed, in which the dynamical system has limit cycles on the zero-energy hypersurfaces. Three types of behavior of the cosmological model have been distinguished, configured by the fundamental constants of the scalar fields and the initial conditions. It is shown that over a wide sector of values of the fundamental constants and initial conditions, the cosmological models have a tendency to adhere to the zero-energy hypersurfaces corresponding to 4-dimensional Euclidean space.