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Bio-economics of a renewable resource subjected to strong Allee effect
Institution:1. Department of Mathematics, Andhra University, Visakhapatnam 530003, India;2. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208016, India;1. University of Central Florida, Department of Mathematics, 4000 Central Florida Blvd., Orlando, USA;2. University of Palermo, Department of Mathematics and Computer Science, Via Archirafi 34, 90123 Palermo, Italy;1. School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, PR China;2. School of Energy and Engineering, Dalian University of Technology, Dalian, Liaoning 116024, PR China;3. School of Environmental and Biological Science and Technology, Dalian University of Technology, Dalian, Liaoning 116012, PR China;1. Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, India;2. Advanced Technological Development Centre, Indian Institute of Technology, Kharagpur 721302, India;1. Faculty of Applied Mathematics, AGH University of Science and Technology, Mickiewicz Avenue 30, 30059 Kraków, Poland;2. Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic;3. Subbotin Institute for Geophysics of NAS of Ukraine, Palladin Avenue 32, 03142 Kyiv, Ukraine
Abstract:In this article bio-economics of a renewable resource that is subjected to strong Allee effect (multiplicative Allee effect) is investigated from sole owner perspective. The considered optimal harvesting problem has been solved using Pontryagin maximum principle. The control problem admits multiple singular equilibrium solutions in contrast to the case where the growth of the resource is of compensatory nature. Thus the choice of optimal singular solution and the nature of associated approach paths make the problem pertinent and interesting.
Keywords:Allee effect  Bio-economics  Multiple singular solutions  Optimal harvest
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