Bifurcation analysis, chaotic structures and wave propagation for nonlinear system arising in oceanography

Ali, Karmina K.; Faridi, Waqas Ali; Yusuf, Abdullahi; El-Rahman, Magda Abd; Ali, Mohamed R.

doi:10.1016/j.rinp.2024.107336

Cited by 10 publications

(1 citation statement)

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“…It often leads to the appearance of new stable states, periodic orbits, or chaotic behavior. Bifurcation theory helps to understand these sudden changes and predict system behavior in different states [ 41 ]. This paragraph offers an overview of the bifurcation and phase diagrams of the upcoming planner dynamic framework.…”

Section: Bifurcation Analysismentioning

confidence: 99%

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

Ullah,

Ali,

Roshid

2024

PLoS ONE

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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.

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Section: Bifurcation Analysismentioning

confidence: 99%