Ulam type stability for von Bertalanffy growth model with Allee effect.

Area of Science:

• Mathematical Biology
• Population Dynamics
• Differential Equations

Background:

• Mathematical models require fitting to real-world data using statistical methods.
• Unstable models can diverge significantly from actual phenomena even with minor perturbations.
• Ulam stability ensures solutions remain close to the original equation under bounded perturbations.

Purpose of the Study:

• To investigate the Ulam stability of the von Bertalanffy growth model incorporating the Allee effect.
• To determine how the Allee effect influences the model's stability.
• To potentially improve existing stability results for the standard von Bertalanffy growth model.

Main Methods:

• Analysis of the von Bertalanffy growth model with the Allee effect.
• Application of Ulam stability theory to the perturbed model.
• Derivation of conditions for Ulam stability based on Allee effect parameters.
• Numerical simulations to illustrate theoretical findings.

Main Results:

• Ulam stability is demonstrated for the von Bertalanffy growth model with the Allee effect.
• The stability is dependent on the magnitude of the Allee effect.
• A superior Ulam constant is achieved as the Allee effect approaches zero, improving upon existing results.
• The study provides enhanced stability guarantees for the model.

Conclusions:

• The von Bertalanffy growth model with the Allee effect is Ulam stable.
• This stability ensures that small perturbations do not drastically alter model solutions.
• The findings offer improved theoretical underpinnings for ecological and biological modeling using this growth function.