| Keywords and phrases: prey-predator, harvest function, fishing effort, Lyapunov function, global stability
Received: February 21, 2024; Accepted: April 18, 2024; Published: July 22, 2024
How to cite this article: Daniel ZAMBELONGO, Moumini KERE and Somdouda SAWADOGO, Optimal harvesting strategy for prey-predator model with fishing effort as a time variable, Advances in Differential Equations and Control Processes 31(3) (2024), 417-438. https://doi.org/10.17654/0974324324023
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License  
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.
|
