Conditional stability of the Schaefer population model

Popa et al. (2018) defined conditional Ulam stability for the logistic equation by obtaining an estimate that scales the difference between the solutions of the exact and perturbed models linearly with the magnitude of the perturbation for perturbations below a certain threshold. In the classical Ulam stability definition, there is no lowvalue condition for the perturbation parameter 𝜀 > 0. In contrast, in conditional Ulam stability, the difference between the solutions of the exact and perturbed models can be estimated to be less than a certain threshold value in the interval [0, ∞), meaning that a low-value condition for 𝜀 > 0 can be found throughout this interval. In this thesis, the conditional Ulam stability of the Schaeffer model, developed for sustainable fish harvest management, is analyzed. In this way, the effect of unpredictable fish losses on the dynamics of the model is demonstrated by determining limits for fish stock and fish loss. The results obtained are supported by examples and simulations