Samreen Maria, Alshammari Fehaid Salem
Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.
PLoS One. 2025 Sep 9;20(9):e0331243. doi: 10.1371/journal.pone.0331243. eCollection 2025.
This research explores the dynamical properties and solutions of actin filaments, which serve as electrical conduits for ion transport along their lengths. Utilizing the Lie symmetry approach, we identify symmetry reductions that simplify the governing equation by lowering its dimensionality. This process leads to the formulation of a second-order differential equation, which, upon applying a Galilean transformation, is further converted into a system of first-order differential equations. Additionally, we investigate the bifurcation structure and sensitivity of the proposed dynamical system. When subjected to an external force, the system exhibits quasi-periodic behavior, which is detected using chaos analysis tools. Sensitivity analysis is also performed on the unperturbed system under varying initial conditions. Moreover, we establish the conservation laws associated with the equation and conduct a stability analysis of the model. Employing the tanh method, we derive exact solutions and visualize them through 3D and 2D graphical representations to gain deeper insights. These findings offer new perspectives on the studied equation and significantly contribute to the understanding of nonlinear wave dynamics.
本研究探索了肌动蛋白丝的动力学性质和解决方案，肌动蛋白丝作为离子沿其长度方向运输的电导体。利用李对称方法，我们识别出对称约化，通过降低其维数来简化控制方程。这个过程导致了一个二阶微分方程的形成，在应用伽利略变换后，它进一步转化为一个一阶微分方程组。此外，我们研究了所提出的动力系统的分岔结构和敏感性。当受到外力作用时，该系统表现出准周期行为，这是使用混沌分析工具检测到的。还在不同初始条件下对未受扰动的系统进行了敏感性分析。此外，我们建立了与该方程相关的守恒定律，并对模型进行了稳定性分析。采用双曲正切方法，我们推导了精确解，并通过三维和二维图形表示将其可视化，以获得更深入的见解。这些发现为所研究的方程提供了新的视角，并对理解非线性波动动力学做出了重大贡献。
