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Modelling and analysis of a harvested prey–predator system incorporating a prey refuge. (English) Zbl 1071.92041
Summary: The present paper deals with a prey-predator model incorporating a prey-refuge and independent harvesting in either species. Our study shows that, using the harvesting efforts as controls, it is possible to break the cyclic behaviour of the system and drive it to a required state. The possibility of existence of bionomic equilibria has been considered. The problem of optimal harvest policies is then solved by using Pontryagin’s maximal principle.
MSC:
92D40Ecology
49N90Applications of optimal control and differential games
34C60Qualitative investigation and simulation of models (ODE)
34C05Location of integral curves, singular points, limit cycles (ODE)