# Bifurcation, chaos, and stability analysis to the second fractional WBBM model

## TL;DR

This paper analyzes the dynamics of a fractional WBBM model to understand bifurcations, chaos, and stability in shallow water waves.

## Contribution

The study introduces novel bifurcation and chaos analysis techniques for a 3D fractional WBBM model using planar dynamic systems.

## Key findings

- The model exhibits quasi-periodic, periodic, and chaotic motion.
- Bright and dark solitons, along with kink and anti-kink waves, are identified.
- Chaos analysis is shown to be crucial for understanding complex system dynamics and stability.

## Abstract

This manuscript investigates bifurcation, chaos, and stability analysis for a significant model in the research of shallow water waves, known as the second 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) model. The dynamical system for the above-mentioned nonlinear structure is obtained by employing the Galilean transformation to fulfill the research objectives. Subsequent analysis includes planar dynamic systems techniques to investigate bifurcations, chaos, and sensitivities within the model. Our findings reveal diverse features, including quasi-periodic, periodic, and chaotic motion within the governing nonlinear problem. Additionally, diverse soliton structures, like bright solitons, dark solitons, kink waves, and anti-kink waves, are thoroughly explored through visual illustrations. Interestingly, our results highlight the importance of chaos analysis in understanding complex system dynamics, prediction, and stability. Our techniques’ efficiency, conciseness, and effectiveness advance our understanding of this model and suggest broader applications for exploring nonlinear systems. In addition to improving our understanding of shallow water nonlinear dynamics, including waveform features, bifurcation analysis, sensitivity, and stability, this study reveals insights into dynamic properties and wave patterns.