Subscribe

Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

IFSL > IFSL Volume 12 > Stability Analysis of a Biological Model of a...
Stability Analysis of a Biological Model of a Marine Resources Allowing Density Dependent Migration
< Back to Volume

Stability Analysis of a Biological Model of a Marine Resources Allowing Density Dependent Migration

Full Text PDF

Abstract:

Biology of a marine resources is a descriptive science. The description is the first step towards understanding a system. However, the main objective is to present a rigorous mathematical analysis and numerical simulation of these spatio temporal models. In the present paper, we consider a two species food chain, i.e. a prey and predator populations modeled in a two-patch environment, one of which is a free fishing zone and the other one is protected zone. We study the qualitative analysis of solutions and we establish sufficient conditions under which the endemic and trivial equilibria are asymptotically stable.The asymptotic stability corresponding to the equilibria is graphically shown.

Info:

Periodical:
International Frontier Science Letters (Volume 12)
Pages:
22-34
DOI:
https://doi.org/10.18052/www.scipress.com/IFSL.12.22
Citation:
M. Bentounsi et al., "Stability Analysis of a Biological Model of a Marine Resources Allowing Density Dependent Migration", International Frontier Science Letters, Vol. 12, pp. 22-34, 2017
Online since:
August 2017
Authors:
Meriem Bentounsi, Imane Agmour, Naceur Achtaich, Youssef El Foutayeni
Keywords:
Biological Equilibrium, Migration, Patches, Prey-Predator Model, Routh Hurwitz Criteria, Stability Properties
Export:
RIS, BibTeX, Text
Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

T.K. Kar, S. Misra, Influence of prey reserve in a prey predator fishery, Nonlinear Analysis: Theory, Methods & Applications. 65(9) (2006) 1725-1735.

DOI: https://doi.org/10.1016/j.na.2005.11.049

J.N. Sanchirico, J.E. Wilen, Bioeconomics of spatial exploitation in a patchy environment, Journal of Environmental Economics and Management. 37(2) (1999) 129-150.

DOI: https://doi.org/10.1006/jeem.1998.1060

P.D.N. Srinivasu, I.L. Gayatri, Influence of prey reserve capacity on predatorprey dynamics, Ecological Modelling. 181(2) (2005) 191-202.

DOI: https://doi.org/10.1016/j.ecolmodel.2004.06.031

B. Dubey, A prey-predator model with a reserved area, Nonlinear Analysis: Modelling and Control. 12 (2007) 479-494.

T.K. Kar, K. Chakraborty, Marine reserves and its consequences as a fisheries management tool, World Journal of Modelling and Simulation. 5 (2009) 83-95.

T. Kar, B. Ghosh, Sustainability and economic consequences of creating marine protected areas in multispecies multiactivity context, Journal of Theoretical Biology. 318 (2013) 81-90.

DOI: https://doi.org/10.1016/j.jtbi.2012.11.004

B. Ghosh et al., Biological conservation through marine protected areas in the presence of alternative stable states, Mathematical Biosciences. 286 (2017) 49-57.

T.K. Kar, K. Chakraborty, Effort dynamics in a prey-predator model with harvesting, International Journal of Information and Systems Sciences. 6(3) (2010) 318-332.

T.K. Kar, A model for fishery resource with reserve area and facing prey-predator interactions, Canadian Applied Mathematics Quarterly. 14(4) (2006) 385-399.

R. Hannesson, The economics of marine reserves, Natural Resource Modeling. 15(3) (2002) 273-290.

O. Flaaten, E. Mjolhus, Using reserves to protect fish and wildlife - simplified modeling approaches, Natural Resource Modeling. 18(2) (2005) 157-182.

DOI: https://doi.org/10.1111/j.1939-7445.2005.tb00153.x

R. Hannesson, Marine Reserves: what would they accomplish?, Marine Resource Economics. 13(3) (1998) 159-170.

DOI: https://doi.org/10.1086/mre.13.3.42629231
Show More Hide
Cited By:

[1] I. Agmour, m. Bentounsi, N. Achtaich, Y. Foutayeni, "Carrying capacity influence on the incomes of seiners exploiting marine species in the Atlantic coast of Morocco", Mathematical Biosciences, 2018

DOI: https://doi.org/10.1016/j.mbs.2018.08.012

[2] Y. El Foutayeni, M. Bentounsi, I. Agmour, N. Achtaich, "Bioeconomic model of zooplankton–phytoplankton in the central area of Morocco", Modeling Earth Systems and Environment, 2019

DOI: https://doi.org/10.1007/s40808-019-00693-w

[3] I. Agmour, M. Bentounsi, N. Baba, Y. El Foutayeni, N. Achtaich, C. Aouiti, "Impact of wind speed on fishing effort", Modeling Earth Systems and Environment, 2020

DOI: https://doi.org/10.1007/s40808-020-00736-7

[4] A. El Bhih, Y. Benfatah, S. Ben Rhila, M. Rachik, A. El Alami Llaaroussi, "A Spatiotemporal Prey-Predator Discrete Model and Optimal Controls for Environmental Sustainability in the Multifishing Areas of Morocco", Discrete Dynamics in Nature and Society, Vol. 2020, p. 1, 2020

DOI: https://doi.org/10.1155/2020/2780651

[5] N. Baba, I. Agmour, Y. El Foutayeni, N. Achtaich, F. Sim es, "Bioeconomic-Epidemiological Model of Scomber colias Population in the Moroccan Coasts", Journal of Applied Mathematics, Vol. 2021, p. 1, 2021

DOI: https://doi.org/10.1155/2021/8892388

[6] I. Agmour, N. Baba, M. Bentounsi, N. Achtaich, Y. El foutayeni, "Mathematical study and optimal control of bioeconomic model concerning harmful dinoflagellate phytoplankton", Computational and Applied Mathematics, Vol. 40, 2021

DOI: https://doi.org/10.1007/s40314-021-01509-3
Show More Hide