Conditional Ulam stability and its application to von Bertalanffy growth model

Masakazu Onitsuka; Masakazu Onitsuka

doi:10.3934/mbe.2022129

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 3: 2819-2834. doi: 10.3934/mbe.2022129

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Research article Special Issues

Conditional Ulam stability and its application to von Bertalanffy growth model

Masakazu Onitsuka ^,

Department of Applied Mathematics, Okayama University of Science, Okayama 700-0005, Japan

Received: 08 November 2021 Revised: 14 December 2021 Accepted: 09 January 2022 Published: 13 January 2022

The purpose of this paper is to apply conditional Ulam stability, developed by Popa, Rașa, and Viorel in 2018, to the von Bertalanffy growth model $ \frac{dw}{dt} = aw^{\frac{2}{3}}-bw $, where $ w $ denotes mass and $ a > 0 $ and $ b > 0 $ are the coefficients of anabolism and catabolism, respectively. This study finds an Ulam constant and suggests that the constant is biologically meaningful. To explain the results, numerical simulations are performed.
- perturbation,
- von Bertalanffy model,
- growth model,
- nonlinear differential equation,
- conditional Ulam stability,
- Ulam constant
Citation: Masakazu Onitsuka. Conditional Ulam stability and its application to von Bertalanffy growth model[J]. Mathematical Biosciences and Engineering, 2022, 19(3): 2819-2834. doi: 10.3934/mbe.2022129

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Abstract

The purpose of this paper is to apply conditional Ulam stability, developed by Popa, Rașa, and Viorel in 2018, to the von Bertalanffy growth model $ \frac{dw}{dt} = aw^{\frac{2}{3}}-bw $, where $ w $ denotes mass and $ a > 0 $ and $ b > 0 $ are the coefficients of anabolism and catabolism, respectively. This study finds an Ulam constant and suggests that the constant is biologically meaningful. To explain the results, numerical simulations are performed.

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