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<p>Mathematical modelling is one of the most effective methods used to explain the interactionsbetween species in ecosystem. Mathematical models of prey-predator systems have been researched bymany ecologists because they are related to human behaviours and ecological life. These systems cannotbe solved analytically, so numerical techniques have been developed to find the approximate solutions.Prey-predator models can be seen as the building blocks of ecology. Therefore, we have been investigateda prey-predator problem that predator density is subjected to harvesting. Harvesting can be two fold in theprey-predator problem. The main purpose is optimal use of the harvested stock to increase the profit. In thiswork, some numerical methods such as Runge-Kutta method, Theta method, Nonstandard Finite Differencemethod, have been proposed to observe the dynamic properties and the stability of the equilibrium pointsin the system. Among the numerical methods that we have been compared, it was seen that the nonstandardfinite difference discretization based on Micken’s rules, gave more accurate results with the use of arbitrarytime step-size. One of the advantages of this method is that better results can be found with the appropriatedenominator function. Also, this new scheme preserves the stability of the equilibrium points and the mainfeatures such as positivity of the continuous system. Therefore it provides reliable numerical results. In thisstudy, numerical simulations have been presented to see the effectiveness of the methods. The effect oftime step size on numerical methods were shown with the help of the tables. Also phase portraits weredrawn.Keywords – Dynamic Consistency, Local Stability, Equilibrium Points, Nonstandard Finite Difference Scheme, NumericalMethods.. <br></p> |
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