Rhythmic behaviors of the human heart with piecewise derivative

Abdon Atangana; Seda İĞRET ARAZ; Abdon Atangana; Seda İĞRET ARAZ

doi:10.3934/mbe.2022143

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 3: 3091-3109. doi: 10.3934/mbe.2022143

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Rhythmic behaviors of the human heart with piecewise derivative

Abdon Atangana ^{1,2
,
,},
Seda İĞRET ARAZ ^1,3

1.
Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
3.
Faculty of Education, Siirt University, Siirt, 56100, Turkey

Received: 06 October 2021 Revised: 29 October 2021 Accepted: 16 November 2021 Published: 19 January 2022

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.
- crossover behaviors,
- piecewise derivative,
- piecewise integral,
- heart rhythm
Citation: Abdon Atangana, Seda İĞRET ARAZ. Rhythmic behaviors of the human heart with piecewise derivative[J]. Mathematical Biosciences and Engineering, 2022, 19(3): 3091-3109. doi: 10.3934/mbe.2022143

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Abstract

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.

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