Abstract
In our present paper, we formulate and study a prey-predator system with imprecise values for the parameters. We also consider harvesting for both the prey and predator species. Then we describe the complex dynamics of the proposed model system including positivity and uniform boundedness of the system, and existence and stability criteria of various equilibrium points. Also the existence of bionomic equilibrium and optimal harvesting policy are thoroughly investigated. Some numerical simulations have been presented in support of theoretical works. Further the requirement of considering imprecise values for the set of model parameters is also highlighted.
Highlights
The eternal relationship between prey and predators is one of the major topics to be discussed in recent science
With the help of mathematical modeling, one can describe the strong and competitive relationship between these two types of creatures. The discussion on this fascinating topic, with the help of some mathematical tool, was started during the first quarter of the twentieth century, thanks to the age-breaking works of Lotka [1] and Volterra [2]. Influenced by those works, researchers are still engaged in theoretical study of the ecological system with the help of mathematical modeling
May [5] has considered and analyzed some other types of ecological systems including prey-predator dynamics, with the help of some sophisticated mathematical models, which are comparatively complex in nature
Summary
The eternal relationship between prey and predators is one of the major topics to be discussed in recent science. May [5] has considered and analyzed some other types of ecological systems including prey-predator dynamics, with the help of some sophisticated mathematical models, which are comparatively complex in nature. From a bioeconomic point of view, harvesting on a species should be in a balance to both keep the resource live and keep fishermen in profitable mode In his two books Clark [22, 23] describes different harvesting policies in some realistic ecological systems with optimal outcome. In this regard, in our present article, we consider a prey-predator type ecological system with harvesting on Journal of Optimization both the species.
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