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Optimal harvesting of a two species competition model with imprecise biological parameters

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Abstract

In this paper a two competing species harvesting model with imprecise biological parameters has been developed. We have developed a method to handle these imprecise parameters and discuss the dynamical behaviour of the model. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. Also the bionomic equilibrium of the harvesting model has been analysed. Next the equilibrium solution of the control problem has been derived, and then dynamical optimization of the harvest policy is carried out taking combined harvesting effort as a dynamic variable by invoking Pontryagin’s Maximum Principle. Our important analytical findings are illustrated through computer simulation using MATLAB followed by discussions and conclusions.

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Acknowledgments

We are grateful to the anonymous referees and the Editor for their careful reading, valuable comments and helpful suggestions which have helped us to improve the presentation of this work significantly.

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  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah , 711 103, India

    Swarnali Sharma & G. P. Samanta

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  1. Swarnali Sharma
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  2. G. P. Samanta
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Correspondence to G. P. Samanta.

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Sharma, S., Samanta, G.P. Optimal harvesting of a two species competition model with imprecise biological parameters. Nonlinear Dyn 77, 1101–1119 (2014). https://doi.org/10.1007/s11071-014-1354-9

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