Self-organized Hydrodynamics in an Annular Domain: Modal Analysis and Nonlinear Effects

TL;DR

This paper analyzes the stability and nonlinear dynamics of the Self-Organized Hydrodynamics model on an annular domain, using modal analysis and numerical simulations to understand collective behavior and mode interactions.

Contribution

It provides a detailed modal analysis of the linearized model and demonstrates the effectiveness of modal decomposition in studying nonlinear features.

Findings

The linearized model has only pure imaginary modes, indicating stability.

Numerical computations of low-order modes are presented.

Modal decomposition effectively analyzes complex nonlinear behaviors.

Abstract

The Self-Organized Hydrodynamics model of collective behavior is studied on an annular domain. A modal analysis of the linearized model around a perfectly polarized steady-state is conducted. It shows that the model has only pure imaginary modes in countable number and is hence stable. Numerical computations of the low-order modes are provided. The fully non-linear model is numerically solved and nonlinear mode-coupling is then analyzed. Finally, the efficiency of the modal decomposition to analyze the complex features of the nonlinear model is demonstrated.