OPTIMAL HARVESTING STRATEGY FOR PREY-PREDATOR MODEL WITH FISHING EFFORT AS A TIME VARIABLE

Daniel ZAMBELONGO; Moumini KERE; Somdouda SAWADOGO

doi:10.17654/0974324324023

Daniel ZAMBELONGO Laboratoire d'Analyse Numériques d'Informatiques et de Biomathématiques, Départementde Mathématiques, UniversitéJoseph KI-ZERBO, 03 BP 7021,Burkina Faso
Moumini KERE Laboratoire d'Analyse Numériques d'Informatiques et de Biomathématiques, Departement de Mathématiques, Ecole Normale Supérieure, 01 BP 1757 Ouaga 01, Burkina Faso
Somdouda SAWADOGO Departementde Mathématiques (Institut Science et Technologie), EcoleNormale Supérieure, 01 BP 1757 Ouaga 01, Burkina Faso

Article ID: 2446

DOI: https://doi.org/10.17654/0974324324023

Keywords: prey-predator, harvest function, fishing effort, Lyapunov function, global stability

Abstract

We study a prey-predator model with harvesting where the fishing effort is considered as a function of time. The analysis focuses on the equilibrium points and the optimal harvesting strategy.

References

[1]Abhijit Sarkar et al., Chaos in a nonautonomous mode for the interactions of prey and predator with effect of water level fluctuation, Journal of Biological Systems 28 (2020), 865-900. doi:10.1142/S0218339020500205.

[2]A. F. Nindjin and M. A. Aziz-Alaoui, Persistence and global stability in a delayed Leslie-Gower type three species food chain, J. Math. Anal. Appl. 340 (2008), 340-357.

[3]A. F. Nindjin, M. A. Aziz-Alaoui and M. Cadevel, Analysis of a predator-prey with modified Leslie-Gower and Holling-type II schemes with time delay, Nonlinear Anal. Real World Appl. 7 (2006), 1104-1118.

[4]A. Moussaoui and S. M. Bouguima, A prey predator interaction under fluctuating level water, Math. Methods Appl. Sci. 38 (2014), 123-137.

[5]A. Moussaoui, S. Bassaid and EL Hadi Ait Dads, The impact of water level fluctuations on a delayed prey-predator model, Nonlinear Anal. Real World Appl. 21 (2015), 170-184.

[6]Ali Moussaoui, A reaction-diffusion equations modelling the effect of fluctuating water levels on prey-predator interactions, Appl. Math. Comput. 268 (2015), 1110-1121.

[7]Baba Issa Camara and M. A. Aziz-Alaoui, Dynamics of a predator-prey model with diffusion, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 15 (2008), 897-906.

[8]Bassaid SIHAM, Modélisation mathématique de quelques problèmes de dynamique des populations, Thèse, 2017.

[9]Colin W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources, 2nd ed., John Wiley and Sons, New York, 1990.

[10]J. C. Seijo, O. Defeo and S. Salas, Fisheries Bioeconomics: Theory, Modelling and Management, FAO, 1997.

[11]Jean-Pierre Demailly, Analyse numérique et équations différentielles, Grenoble Science, 2006.

[12]K. Belkhodja, A. Moussaoui and M. A. Aziz Alaoui, Optimal harvesting and stability for a prey predator model, Nonlinear Anal. Real World Appl. 39 (2017), 321-336.

[13]K. Chakraborty, K. Das and T. K. Kar, Combined harvesting of a stage structured prey-predator model incorporating cannibalism in competitive environment, C. R. Biologies 336 (2013), 34-45.

[14]K. Chakraborty, S. Jana and T. K. Kar, Global dynamics and bifurcation in a stage structured prey-predator fishery model with harvesting, Appl. Math. Comput. 218 (2012), 9271-9290.

[15]Leed G. Anderson and Juan Carlos Seijo, Bioeconomics of Fisheries Management, Wiley, 2010.

[16]M. Kot, Elements of Mathematical Ecology, Cambridge University Press, 2001.

[17]Na Zhang, Y. Kao, F. Chen, B. Xie and S. Li, On a predator-prey system interaction under fluctuation water level with nonselective harvesting, Open Mathematics 18 (2020), 458-475.

[18]N. Chilboud Fellah, S. M. Bouguima and A. Moussaoui, The effect of water level in a prey-predator interactions: a nonlinear analysis study, Chaos Solutions Fractals 45 (2012), 205-212.

[19]Pierre Auger, Étude mathématique en écologie, Dunod, Paris, 2010.

[20]Suzanne Lenhart and John T. Workman, Optimal Control Applied to Biological Models, Chapman and Hall/CRC, New York, 2007.

[21]Suzanne Touzeau, Modèles de contrôle en gestion des pêches, 1997.

[22]Wendell H. Fleming and Raymond W. Rishel, Deterministic and Stochastic Optimal Control, Springer-Verlag, New York, 1975.