In this paper, a complete non-linear symmetric oscillator model using the Hamiltonian approach has been developed and used to describe the cardiovascular conduction process’s dynamics, as the signal generated from the cardiovascular muscle is non-deterministic and random. Electrocardiogram (ECG) signal is a significant factor in the cardiovascular system as most of the medical diagnoses can be well understood by observing the ECG signal’s amplitude. A non-linear cardiovascular muscle model has been proposed in this study, where a modified vanderPol symmetric oscillator-based equation is used. Gone are the days whena non-linear system had been designed using the describing function technique. It is better to design a non-linear model using the Hamiltonian dynamical equation for its high accuracy and flexibility. Varying a non-linear spring constant using this type of approach is more comfortable than the traditional describing function technique. Not only that but different initial conditions can also be taken for experimental purposes. It never affects the overall modeling. The Hamiltonian approach provides the energy of an asymmetric oscillatory system of that cardiovascular conduction system. A non-linear symmetric oscillator was initially depicted by the non-linear mass-spring (two degrees of freedom) model. The motion of an uncertain non-linear cardiovascular system has been solved considering second-order approximation, which also demonstrates the possibility of introducing spatial dimensions. Finally, the model’s natural frequency expression has also been simulated and is composed of the previously published result.

中文翻译：

---

使用非线性对称振荡器的心血管肌肉动力学

在本文中，已经开发了使用汉密尔顿方法的完整非线性对称振荡器模型，并用于描述心血管传导过程的动力学，因为从心血管肌肉产生的信号是不确定的且随机的。心电图（ECG）信号是心血管系统中的重要因素，因为通过观察ECG信号的幅度可以很好地理解大多数医学诊断。在这项研究中提出了一种非线性心血管肌肉模型，其中使用了一个基于vanderPol对称振荡器的改进方程。使用描述函数技术设计非线性系统的日子已经一去不复返了。最好使用哈密顿动力学方程设计非线性模型，因为它具有很高的准确性和灵活性。使用这种方法来改变非线性弹簧常数比传统的描述函数技术更舒适。不仅如此，还可以将不同的初始条件用于实验目的。它永远不会影响整体建模。哈密​​顿方法提供了该心血管传导系统的非对称振荡系统的能量。非线性对称振荡器最初是由非线性质量弹簧（两个自由度）模型描述的。考虑到二阶逼近，已经解决了不确定的非线性心血管系统的运动，这也证明了引入空间尺寸的可能性。最后，还模拟了模型的固有频率表达式，该模型由先前发布的结果组成。