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Conditional Ulam stability and its application to von Bertalanffy growth model.
1Department of Applied Mathematics, Okayama University of Science, Okayama 700-0005, Japan.
Mathematical Biosciences and Engineering : MBE
|March 4, 2022
Summary
This study applies conditional Ulam stability to the von Bertalanffy growth model, finding a biologically meaningful Ulam constant. Numerical simulations explain these results for growth dynamics.
Area of Science:
- Mathematical Biology
- Differential Equations
- Numerical Analysis
Background:
- The von Bertalanffy growth model describes organismal growth using differential equations.
- Anabolism and catabolism coefficients ($a$ and $b$) influence growth dynamics.
- Ulam stability provides a framework for analyzing the stability of functional equations.
Purpose of the Study:
- To apply conditional Ulam stability to the von Bertalanffy growth model.
- To determine the Ulam constant for this specific biological model.
- To investigate the biological significance of the Ulam constant.
Main Methods:
- Application of conditional Ulam stability theory.
- Analysis of the differential equation $dw/dt = aw^{2/3} - bw$.
- Conducting numerical simulations to illustrate findings.
Main Results:
- An Ulam constant was successfully identified for the von Bertalanffy growth model.
- The determined Ulam constant demonstrates biological relevance.
- Numerical simulations validated the theoretical results.
Conclusions:
- Conditional Ulam stability is applicable to biological growth models.
- The Ulam constant offers new insights into growth parameter stability.
- Further research can explore Ulam stability in other biological models.
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