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IJSTR >> Volume 8 - Issue 7, July 2019 Edition



International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616



A Prey-Predator Fishery Model With A Relative Size Of Reserved Area

[Full Text]

 

AUTHOR(S)

Kulbhushan Agnihotri, Sheenu Nayyer

 

KEYWORDS

Relative size; Holling type II; Migration; Optimal harvesting; Pontryagin's Maximum Principle; MPAs.

 

ABSTRACT

A prey-predator fishery model having reserved and unreserved area, with prey dispersal in a two-patch environment, has been proposed and investigated in this work. The logistic growth is considered for the fish species in each area. Holling type-II predator functional response has been considered. Relative size of the reserve and unreserved area is responsible for increase as well as decrease the density of the fishes. The harvesting is applied on both prey in an unreserved area and on predator. The dynamics of the proposed system has been explored locally. The thresholds for existence of biological equilibrium points are obtained. Optimal harvesting policy has been examined by the Pontryagin's Maximum Principle. Finally, theoretical results acquired and verified with the assistance of numerical simulations through MATLAB.

 

REFERENCES

[1] K. Hartmann, L. Bode, P. Armsworth. “The economic optimality of learning from marine protected areas,”ANZIAM, , 48: pp 307–329, 2007.
[2] U. Sumalia. “Marine protected area performance in a model of the fishery,” Natural Resource Modeling, 15(4), 2002.
[3] Takashina, N., Mougi, A., Iwasa, Y. “Paradox of marine protected areas: suppression of fishing may cause species loss,” Popul. Ecol. 54(3), pp 475–485, 2012.
[4] Kar, T. K., & Matsuda, H, “A bioeconomic model of a single-species fishery with a marine reserve,” Journal of environmental management, 86(1), pp 171-180, 2008.
[5] Chakraborty, K., Das, K., & Kar, T. K, “An ecological perspective on marine reserves in prey–predator dynamics,” Journal of biological physics, 39(4), pp 749-776, 2013.
[6] Dubey, B., Chandra, P., & Sinha, P, “A model for fishery resource with reserve area,” Nonlinear Analysis: Real World Applications, 4(4), pp 625-637, 2003.
[7] Lv, Y., Yuan, R., & Pei, Y. “A prey-predator model with harvesting for fishery resource with reserve area,” Applied Mathematical Modelling, 37(5), pp 3048-3062, 2013.
[8] Dubey,B.“A prey-predator model with a reserved area,” Nonlinear Analysis: Modelling and Control, 12(4), pp 479-494, 2007.
[9] Arrow, K. J., & Kruz, M. “Public investment, the rate of return, and optimal fiscal policy,” (Vol. 1). Routledge. 12(4). pp. 479-494, 2013.
[10] B., & Hussain, J. “Modelling the survival of species dependent on a resource in a polluted environment,” Nonlinear analysis: real world applications, 7(2), pp 187-210, 2006.
[11] Dubey, B., & Narayanan, A. S. “Modelling effects of industrialization, population and pollution on a renewable resource,” Nonlinear Analysis: Real World Applications, 11(4), pp 2833-2848, 2010.
[12] Dubey, B., Sharma, S., Sinha, P., & Shukla, J. B. “Modelling the depletion of forestry resources by population and population pressure augmented industrialization,” Applied Mathematical Modelling, 33(7), pp 3002-3014, 2009.
[13] Kar, T. K., & Chaudhuri, K. S. “On non-selective harvesting of two competing fish species in the presence of toxicity,” Ecological Modelling, 161(1-2), pp 125-137. 2003.
[14]N. Juneja and K.Agnihotri, “Global Stability of Harvested Prey–Predator Model with Infection in Predator Species,” In Information and Decision Sciences, Springer, Singapore , pp 559-568, 2018.
[15] N. Juneja, K. Agnihotri and H. Kaur, “Effect of delay on globally stable prey-predator system,” Chaos, Solitons & Fractals, 111, pp 146–156, 2018.
[16] Nayyar, S., & Agnihotri, D. K, “A study of migrating prey (fish)-predator (bird) fishery resource with reserve and unreserved area”, International Journal of Research and Analytical Reviews (IJRAR), 5(3), pp 382-389, 2018.
[17] Agnihotri, K, Nayyer S., “ Stability analysis of a predator (bird) –prey (fish)harvesting model in the reserved and unreserved area”, Malaya Journal of Matematik, Vol. 6, No. 3, pp 678-684, 2018.
[18] Madhusudhan Reddy K., Lakshmi Narayan K. and Ravindra Reddy B. “Dynamics of an SEIR Epidemic Model with Time Delay”, Journal of Advanced Research in Dynamical and Control Systems, Vol. 11, Issue no 1, pp 102-108, 2019.
[19] Evuri Suryanarayana and Lakshmi Narayan K, “Dynamics of Prey, Predator and Commensalism Model with Time Delay”, Journal of Advanced Research in Dynamical and Control Systems, Vol. 11, Issue no 1, pp 122-131, 2019.
[20] Hui Miao, and Chengjun Kang, "Stability and Hopf Bifurcation Analysis of an HIV Infection Model with Saturation Incidence and Two Time Delays," Engineering Letters, vol. 27, no.1, pp 9-17, 2019.
[21] Zaowang Xiao, and Zhong Li, "Stability and Bifurcation in a Stage-structured Predator-prey Model with Allee Effect and Time Delay," IAENG International Journal of Applied Mathematics, vol. 49, no.1, pp 6-13, 2019