Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
Math Biosci Eng. 2022 Jan 19;19(3):3091-3109. doi: 10.3934/mbe.2022143.
It has been noticed that heartbeats can display different patterns according to situations faced by a human. It has been indicated that, those passages from one pattern to another cannot be modelled using a single differential operator, either classical, fractional, or stochastic. In 2021, alternative concepts were introduced and called piecewise differentiation and integration, these concepts were applied in several complex problems with great insight. It is strongly believed that such will be leading concepts to modelling real-world problems with crossover behaviors. Crossover behaviors have been observed in heart rhythm, therefore, in this paper, the well-known van Der Pol equation will be subjected to piecewise analysis. Several simulations will be obtained using a numerical scheme based on Newton polynomial interpolation. Obtained figures show real world behaviors of heart rhythm with piecewise patterns.
已经注意到，心跳可以根据人类面临的情况显示出不同的模式。已经表明，从一种模式到另一种模式的这些转变不能使用单个微分算子（无论是经典的、分数的还是随机的）来建模。在 2021 年，引入了替代概念，并称为分段微分和积分，这些概念在几个复杂问题中得到了很好的应用。人们强烈认为，这些概念将成为解决具有交叉行为的现实世界问题的主要方法。已经在心律中观察到了交叉行为，因此，在本文中，将对著名的范德波尔方程进行分段分析。将使用基于牛顿多项式插值的数值方案获得几个模拟。得到的图形显示了具有分段模式的心律的真实世界行为。
