Optimal control for a size-structured predator-prey model in a polluted environment

Tainian Zhang; Zhixue Luo

doi:10.1051/e3sconf/202126901004

All issues

Volume 269 (2021)

E3S Web Conf., 269 (2021) 01004

References

Open Access

Issue		E3S Web Conf. Volume 269, 2021 2021 International Conference on Environmental Engineering, Agricultural Pollution and Hydraulical Studies (EEAPHS 2021)


Article Number		01004
Number of page(s)		8
Section		Environmental Engineering
DOI		https://doi.org/10.1051/e3sconf/202126901004
Published online		09 June 2021

T. G. Hallam, C. E. Clark, R. R. Lassiter. Effects of toxicants on population: A qualitative approach I. Equilibrium environmental exposure. Ecol. Model., 18: 291-304 (1983) [Google Scholar]
T. G. Hallam, C. E. Clark, G. S. Jordan. Effects of toxicants on populations: A qualitative approach II. First order kinetics. J. Math. Biol., 18: 25-37 (1983) [Google Scholar]
T. G. Hallam, J. T. De Luna. Effects of toxicants on populations: A qualitative approach III. Environmental and food chain pathways. J. theor. Biol., 109: 411-429 (1984) [Google Scholar]
Z. X. Luo, Z. R. He. Optimal control of agedependent population hybrid system in a polluted environment. Appl. Math. Comput., 228: 68-76 (2014) [Google Scholar]
H. Wang, F. M. Pan, M. Liu. Survival analysis of a stochastic service–resource mutualism model in a polluted environment with pulse toxicant input. Physica A, 521: 591-606 (2019) [Google Scholar]
G. D. Liu, X. Z. Meng. Optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching. Physica A, 536: 120893 (2019) [Google Scholar]
S. Anita. Analysis and Control of Age-Dependent Population Dynamics. Kluwer Academic Publishers, Dordrecht (2000) [Google Scholar]
Y. J. Li, Z. H. Zhang, Y. F. Lv, et al. Optimal harvesting for a size-stage-structured population model. Nonlinear Anal. Real World Appl., 44: 616-630 (2018) [Google Scholar]
J. Liu, X. S. Wang. Numerical optimal control of a size-structured PDE model for metastatic cancer treatment. Math. Biosic., 314: 28-42 (2019) [Google Scholar]
A. Skonhoft, V. Friberg. Optimal harvesting in the presence of predation: An age-structured modelling approach. J. Environ. Manage., 227: 111-341 (2021) [Google Scholar]
Z. R. He, R. Liu. Theory of optimal harvesting for a nonlinear size-structured population in periodic environments. Int. J. Biomath., 7: 1450046 (2014) [Google Scholar]
F. Q. Zhang, R. Liu, Y. M. Chen. Optimal harvesting in a periodic food chain model with size structures in predators. Appl. Math. Optim., 75: 229-251 (2017) [Google Scholar]
L. I. Anita, S. Anita. Note on some periodic optimal harvesting problems for age-structured population dynamics. Appl. Math. Comput., 276: 21-30 (2016) [Google Scholar]
Y. Liu, X. L. Cheng, Z. R. He. On the optimal harvesting of size-structured population dynamics. Appl. Math. J. Chinese Univ., 28: 173-186 (2013) [Google Scholar]

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[1] T. G. Hallam, C. E. Clark, R. R. Lassiter. Effects of toxicants on population: A qualitative approach I. Equilibrium environmental exposure. Ecol. Model., 18: 291-304 (1983) [Google Scholar]

[2] T. G. Hallam, C. E. Clark, G. S. Jordan. Effects of toxicants on populations: A qualitative approach II. First order kinetics. J. Math. Biol., 18: 25-37 (1983) [Google Scholar]

[3] T. G. Hallam, J. T. De Luna. Effects of toxicants on populations: A qualitative approach III. Environmental and food chain pathways. J. theor. Biol., 109: 411-429 (1984) [Google Scholar]

[4] Z. X. Luo, Z. R. He. Optimal control of agedependent population hybrid system in a polluted environment. Appl. Math. Comput., 228: 68-76 (2014) [Google Scholar]

[5] H. Wang, F. M. Pan, M. Liu. Survival analysis of a stochastic service–resource mutualism model in a polluted environment with pulse toxicant input. Physica A, 521: 591-606 (2019) [Google Scholar]

[6] G. D. Liu, X. Z. Meng. Optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching. Physica A, 536: 120893 (2019) [Google Scholar]

[7] S. Anita. Analysis and Control of Age-Dependent Population Dynamics. Kluwer Academic Publishers, Dordrecht (2000) [Google Scholar]

[8] Y. J. Li, Z. H. Zhang, Y. F. Lv, et al. Optimal harvesting for a size-stage-structured population model. Nonlinear Anal. Real World Appl., 44: 616-630 (2018) [Google Scholar]

[9] J. Liu, X. S. Wang. Numerical optimal control of a size-structured PDE model for metastatic cancer treatment. Math. Biosic., 314: 28-42 (2019) [Google Scholar]

[10] A. Skonhoft, V. Friberg. Optimal harvesting in the presence of predation: An age-structured modelling approach. J. Environ. Manage., 227: 111-341 (2021) [Google Scholar]

[11] Z. R. He, R. Liu. Theory of optimal harvesting for a nonlinear size-structured population in periodic environments. Int. J. Biomath., 7: 1450046 (2014) [Google Scholar]

[12] F. Q. Zhang, R. Liu, Y. M. Chen. Optimal harvesting in a periodic food chain model with size structures in predators. Appl. Math. Optim., 75: 229-251 (2017) [Google Scholar]

[13] L. I. Anita, S. Anita. Note on some periodic optimal harvesting problems for age-structured population dynamics. Appl. Math. Comput., 276: 21-30 (2016) [Google Scholar]

[14] Y. Liu, X. L. Cheng, Z. R. He. On the optimal harvesting of size-structured population dynamics. Appl. Math. J. Chinese Univ., 28: 173-186 (2013) [Google Scholar]