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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:

92D40 Ecology
49N90 Applications of optimal control and differential games
34C60 Qualitative investigation and simulation of ordinary differential equation models
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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