# Dynamical properties of acoustic-gravity waves in the atmosphere

## TL;DR

This paper investigates the complex dynamical behaviors of acoustic-gravity waves in the atmosphere using nonlinear equations, revealing transitions from ordered to chaotic states influenced by key parameters.

## Contribution

It introduces a detailed analysis of the nonlinear system governing acoustic-gravity waves, highlighting the conditions leading to chaos and the role of the density scale height parameter.

## Key findings

- System can transition from order to chaos based on control parameter s_1.
- Lyapunov exponents indicate chaotic regimes.
- Numerical simulations confirm the interplay between order and chaos.

## Abstract

We study the dynamical behaviors of a system of five coupled nonlinear equations that describes the dynamics of acoustic-gravity waves in the atmosphere. A linear stability analysis together with the analysis of Lyapunov exponents spectra are performed to show that the system can develop from ordered structures to chaotic states. Numerical simulation of the system of equations reveals that an interplay between the order and chaos indeed exists depending on whether the control parameter $s_1$, associated with the density scale height of acoustic-gravity waves, is below or above its critical value.