Optimal harvesting strategy of a stochastic $ n $-species marine food chain model driven by Lévy noises

Nafeisha Tuerxun; Zhidong Teng; Nafeisha Tuerxun; Zhidong Teng

doi:10.3934/era.2023265

Electronic Research Archive

2023, Volume 31, Issue 9: 5207-5225. doi: 10.3934/era.2023265

Previous Article Next Article

Research article Special Issues

Optimal harvesting strategy of a stochastic $ n $-species marine food chain model driven by Lévy noises

Nafeisha Tuerxun ¹,
Zhidong Teng ^{2
,
,}

1.
College of Science, Jimei University, Xiamen 361021, China
2.
College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830017, China

Academic Editor: M. Victoria Otero-Espinar

Received: 24 May 2023 Revised: 30 June 2023 Accepted: 09 July 2023 Published: 19 July 2023

A stochastic $ n $-species marine food chain model with harvesting and Lévy noises is proposed. First, the criterion on the asymptotic stability in distribution is established. Second, the criterion on the existence of optimal harvesting strategy (OHS) and the maximum of expectation of sustainable yield (MESY) are derived. Furthermore, the numerical simulations are presented to verify the theoretical results. Our results show that (i) noises intensity can easily affect the dynamics of marine populations, leading to the imbalances of marine ecology, (ii) the establishment of an optimal harvesting strategy should fully consider the impact of noises intensity for better managing and protecting marine resources.
- stochastic marine food chain model,
- Lévy noises,
- stability in distribution,
- optimal harvesting strategy
Citation: Nafeisha Tuerxun, Zhidong Teng. Optimal harvesting strategy of a stochastic $ n $-species marine food chain model driven by Lévy noises[J]. Electronic Research Archive, 2023, 31(9): 5207-5225. doi: 10.3934/era.2023265

Related Papers:

Abstract

A stochastic $ n $-species marine food chain model with harvesting and Lévy noises is proposed. First, the criterion on the asymptotic stability in distribution is established. Second, the criterion on the existence of optimal harvesting strategy (OHS) and the maximum of expectation of sustainable yield (MESY) are derived. Furthermore, the numerical simulations are presented to verify the theoretical results. Our results show that (i) noises intensity can easily affect the dynamics of marine populations, leading to the imbalances of marine ecology, (ii) the establishment of an optimal harvesting strategy should fully consider the impact of noises intensity for better managing and protecting marine resources.

References

[1]	J. Jeremy, K. Michael, B. Wolfgang, B. Karen, B. Louis, B. Bruce, et al., Historical overfishing and the recent collapse of coastal ecosystems, Science, 293 (2001), 629–637. https://doi.org/10.1126/science.1059199 doi: 10.1126/science.1059199
[2]	A. Myers, B. Worm, Rapid worldwide depletion of predatory fish communities, Nature, 423 (2003), 280–283. https://doi.org/10.1038/nature01610 doi: 10.1038/nature01610
[3]	S. Murawski, Definitions of overfishing from an ecosystem perspective, Ices J. Mar., 57(2000), 649–658. https://doi.org/10.1006/jmsc.2000.0738 doi: 10.1006/jmsc.2000.0738
[4]	M. Scheffer, S. Carpenter, Y. De, Cascading effects of overfishing marine systems, Trends Ecol. Evol., 20 (2005), 579–581. https://doi.org/10.1016/j.tree.2005.08.018 doi: 10.1016/j.tree.2005.08.018
[5]	K. Nicholas, P. Nathan, L. Cassandra, A. Riley A, W. Rima, A. David, et al., Overfishing drives over one-third of all sharks and rays toward a global extinction crisis, Curr. Biol., 31 (2021), 4773–4787. https://doi.org/10.1016/j.cub.2021.08.062 doi: 10.1016/j.cub.2021.08.062
[6]	K. Nicholas, L. Sarah, A. John, D. Rachel, M. Peter, R. Lucy, et al., Extinction risk and conservation of the world¡¯s sharks and rays, eLife, 3 (2014), e00590. https://doi.org/10.7554/eLife.00590 doi: 10.7554/eLife.00590
[7]	C. Clark, Mathematical Bioeconomics: The Optimal Management of Renewal Resources, Wiley Press, New York, 1976.
[8]	A. Martin, S. Ruan, Predator-prey models with delay and prey harvesting, J. Math. Biol., 43 (2001), 247–267. https://doi.org/10.1007/s002850100095 doi: 10.1007/s002850100095
[9]	R. May, Stability and Complextiy in Model Ecosystems, Princeton University Press, Princeton, 2001.
[10]	R. Lande, S. Engen, B. Saether, Stochastic Population Dynamics in Ecology and Conservation, Oxford University Press, Oxford, 2003.
[11]	W. Li, K. Wang, Optimal harvesting policy for general stochastic logistic population model, J. Math. Anal. Appl., 368 (2010), 420-428. https://doi.org/10.1016/j.amc.2011.05.079 doi: 10.1016/j.amc.2011.05.079
[12]	S. Wang, L. Wang, T. Wei, Optimal harvesting for a stochastic predator¨Cprey model with S-type distributed time delays, Methodol. Comput. Appl. Probab., 20 (2018), 37–68. https://doi.org/10.1007/s11009-016-9519-2 doi: 10.1007/s11009-016-9519-2
[13]	L. Jia, X. Liu, Optimal harvesting strategy based on uncertain logistic population model, Chaos Solitons Fractals, 152 (2021), 111329. https://doi.org/10.1016/j.chaos.2021.111329 doi: 10.1016/j.chaos.2021.111329
[14]	W. Giger, The Rhine red, the fish dead-the 1986 Schweizerhalle disaster, a retrospect and long-term impact assessment, Environ. Sci. Pollut. Res., 16 (2009), 98–111. https://doi.org/10.1007/s11356-009-0156-y doi: 10.1007/s11356-009-0156-y
[15]	C. Campagna, F. Short, B. Polidoro, R. McManus, B. Collette, N. Pilcher, et al., Gulf of Mexico Oil Blowout increases risks to globally threatened species, BioSci., 61 (2011), 393–397. https://doi.org/10.1525/bio.2011.61.5.8 doi: 10.1525/bio.2011.61.5.8
[16]	J. Bao, X. Mao, G. Yin, C. Yuan, Competitive Lotka-Volterra population dynamics with jumps, Nonlinear Anal. Theor., 74 (2011), 6601–6616. https://doi.org/10.1016/j.na.2011.06.043 doi: 10.1016/j.na.2011.06.043
[17]	X. Zhang, K. Wang, Stochastic SIR model with jumps, Appl. Math. Lett., 26 (2013), 867–874. https://doi.org/10.1016/j.aml.2013.03.013 doi: 10.1016/j.aml.2013.03.013
[18]	T. Nafeisha, Z. Teng, M. Ahmadjan, Global dynamics in a stochastic three species food-chain model with harvesting and distributed delays, Adv. Differ. Equations, 2019 (2019), 187. https://doi.org/10.1186/s13662-019-2122-4 doi: 10.1186/s13662-019-2122-4
[19]	T. Nafeisha, Z. Teng, W. Chen, Dynamic analysis of a stochastic four species food-chain model with harvesting and distributed delay, Bound. Value Prob., 2021 (2021), 12. https://doi.org/10.1186/s13661-021-01487-9 doi: 10.1186/s13661-021-01487-9
[20]	T. Nafeisha, Z. Teng, Global dynamics in stochastic n-species food chain systems with white noise and Lévy jumps, Math. Methods Appl. Sci., 45 (2022), 5184–5214. https://doi.org/10.1002/mma.8101 doi: 10.1002/mma.8101
[21]	Y. Shao, Dynamics and optimal harvesting of a stochastic predator-prey system with regime switching, S-type distributed time delays and Lévy jumps.AIMS Math., 7 (2022), 4068–4093. https://doi.org/10.3934/math.2022225
[22]	I. Barbalat, Systeme d¡±equations differentielles d¡±oscillations non lineaires. Rev. Roum. Math. Pures, 4 (1959), 260–270.
[23]	G. Prato, J. Zabczyk, Ergodicity for infinite dimensional systems, Cambridge University Press, Cambridge, 1996.

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)