Department of Mathematics, Comilla University, Cumilla, Bangladesh.
Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh.
PLoS One. 2024 Jul 23;19(7):e0307565. doi: 10.1371/journal.pone.0307565. eCollection 2024.
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.
本文研究了浅水波研究中一个重要模型的分岔、混沌和稳定性分析，即第二三维分数 Wazwaz-Benjamin-Bona-Mahony（WBBM）模型。通过运用伽利略变换获得上述非线性结构的动力系统，以实现研究目标。随后的分析包括平面动力系统技术，以研究模型中的分岔、混沌和敏感性。我们的发现揭示了不同的特征，包括在控制非线性问题中的准周期、周期和混沌运动。此外，通过可视化插图，还深入研究了不同的孤子结构，如亮孤子、暗孤子、扭波和反扭波。有趣的是，我们的结果强调了混沌分析在理解复杂系统动力学、预测和稳定性方面的重要性。我们的技术的效率、简洁性和有效性提高了我们对该模型的理解，并为探索非线性系统提供了更广泛的应用。除了提高我们对包括波形特征、分岔分析、敏感性和稳定性在内的浅水波非线性动力学的理解之外，这项研究还揭示了对动态特性和波型的深入了解。
