An optimal control of the predation model

الملخص EN

This paper presents an extension to the predation model using the optimal control theory to obtain the optimal paths for the prey and predator levels for each type.

These levels were represented as state variables for the optimal control problem, and also for the optimal paths for the levels of other prey and predator which were represented as control variables.

In this direction, we will use the Maple program to solve the numerically controlled system based on nonlinear ordinary differential equations and using some constraints on the prey and predator numbers.

The objective function is determined to reduce the lost numbers of all prey and predator at the end of the predation period to a minimum value in specific area.

There are three different cases examined to reflect the effect of presence or absence the carrying capacity for the prey, and the effect of presence non-natural deterioration for the two species, and finally the effect of additional migration of two species.