Hopf bifurcation in a delayed differential-algebraic biological economic system
This paper deals with a predator-prey differential system incorporating harvesting effort on the prey and a constant time delay which represents the reaction time of the preys. The model is completed with an algebraic equation which incorporates the economic effect of harvesting, according to the economic theory proposed by Gordon in 1954. The main goal of the paper is to analyze the behaviour of the positive steady-state of this differential-algebraic system in terms of the delay considered as a varying parameter. Using the general theory of normal forms and the center manifold theory, the existence of a Hopf bifurcation is analyzed. The paper includes some numerical simulations to illustrate the analytical findings.
scientific article; zbMATH DE number 5882900
scientific article