Randomness Effect on a Fish Population Model Using Gumbel Distribution
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Fish population model, Gumbel distribution, Randomness, Uncertainty, Stability.
Abstract
Uncertainty in mathematical models has been raised in the last period. It can be happened due to insuf?cient knowledge about particular components of the model. Probability theory is a powerful tool can be applied to treat many of these problems. In this work, the effects of randomness on the fish population model are studied. The Gumbel distribution is chosen to explore the uncertainty in the model by considering the initial population sizes and the harvesting parameter of the deterministic model as the located parameter of the distribution. Discussion is given and the stability of the equilibrium points is studied. Furthermore, the random behaviour of the population and its statistical properties are investigated and compared with the deterministic behaviour.
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