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Optimal harvesting policy for the Beverton--Holt model
1. | Missouri University of Science and Technology, 400 West, 12th Street, Rolla, MO 65409-0020, United States, United States |
References:
[1] |
L. Bai and K. Wang, A diffusive single-species model with periodic coefficients and its optimal harvesting policy, Appl. Math. Comput., 187 (2007), 873-882.
doi: 10.1016/j.amc.2006.09.007. |
[2] |
J. Barić, R. Bibi, M. Bohner, A. Nosheen and J. Pečarić, Jensen inequalities on time scales, in Monographs in Inequalities, ELEMENT, Zagreb, Volume 9, 2015. |
[3] |
L. Berezansky and E. Braverman, On impulsive Beverton-Holt difference equations and their applications, J. Differ. Equations Appl., 10 (2004), 851-868.
doi: 10.1080/10236190410001726421. |
[4] |
R. J. H. Beverton and S. J. Holt, On the Dynamics of Exploited Fish Populations, Fish & Fisheries Series, 1993.
doi: 10.1007/978-94-011-2106-4. |
[5] |
D. K. Bhattacharya and S. Begum, Bionomic equilibrium of two-species system. I, Math. Biosci., 135 (1996), 111-127.
doi: 10.1016/0025-5564(95)00170-0. |
[6] |
M. Bohner and R. Chieochan, The Beverton-Holt $q$-difference equation, J. Biol. Dyn., 7 (2013), 86-95. |
[7] |
M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser Boston, Inc., Boston, MA, 2001.
doi: 10.1007/978-1-4612-0201-1. |
[8] |
M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser Boston, Inc., Boston, MA, 2003.
doi: 10.1007/978-0-8176-8230-9. |
[9] |
M. Bohner, S. Stević and H. Warth, The Beverton-Holt difference equation, in Discrete dynamics and difference equations, World Sci. Publ., Hackensack, NJ, (2010), 189-193.
doi: 10.1142/9789814287654_0012. |
[10] |
M. Bohner and S. H. Streipert, The Beverton-Holt equation with periodic growth rate, Int. J. Math. Comput., 26 (2015), 1-10. |
[11] |
M. Bohner and S. H. Streipert, The Beverton-Holt $q$-difference equation with periodic growth rate, in Difference equations, discrete dynamical systems, and applications, Springer-Verlag, Berlin-Heidelberg-New York, 150 (2015), 3-14.
doi: 10.1007/978-3-319-24747-2_1. |
[12] |
M. Bohner and H. Warth, The Beverton-Holt dynamic equation, Appl. Anal., 86 (2007), 1007-1015.
doi: 10.1080/00036810701474140. |
[13] |
E. Braverman and L. Braverman, Optimal harvesting of diffusive models in a nonhomogeneous environment, Nonlinear Anal., 71 (2009), e2173-e2181.
doi: 10.1016/j.na.2009.04.025. |
[14] |
E. Braverman and R. Mamdani, Continuous versus pulse harvesting for population models in constant and variable environment, J. Math. Biol., 57 (2008), 413-434.
doi: 10.1007/s00285-008-0169-z. |
[15] |
C. W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources, John Wiley & Sons, Inc., New York, 1990. |
[16] |
T. Diagana, Almost automorphic solutions to a Beverton-Holt dynamic equation with survival rate, Appl. Math. Lett., 36 (2014), 19-24.
doi: 10.1016/j.aml.2014.04.011. |
[17] |
M. Fan and K. Wang, Optimal harvesting policy for single population with periodic coefficients, Math. Biosci., 152 (1998), 165-177.
doi: 10.1016/S0025-5564(98)10024-X. |
[18] |
B.-S. Goh, Management and Analysis of Biological Populations, Volume 8, Elsevier North-Holland, Inc., New York, NY, 1980. |
[19] |
M. Holden, Beverton and Holt revisited, Fisheries Research, 24 (1995), 3-8.
doi: 10.1016/0165-7836(95)00377-M. |
[20] |
W. Kelley and A. Peterson, Difference Equations: An Introduction with Applications, Academic Press, Inc., Boston, MA, 1991. |
[21] |
C. Kent, V. Kocic and Y. Kostrov, Attenuance and resonance in a periodically forced sigmoid Beverton-Holt model, Int. J. Difference Equ., 7 (2012), 35-60. |
[22] |
V. L. Kocic, A note on the nonautonomous Beverton-Holt model, J. Difference Equ. Appl., 11 (2005), 415-422.
doi: 10.1080/10236190412331335463. |
[23] |
V. L. Kocic and Y. Kostrov, Dynamics of a discontinuous discrete Beverton-Holt model, J. Difference Equ. Appl., 20 (2014), 859-874.
doi: 10.1080/10236198.2013.824968. |
[24] |
A. W. Leung, Optimal harvesting-coefficient control of steady-state prey-predator diffusive Volterra-Lotka systems, Appl. Math. Optim., 31 (1995), 219-241.
doi: 10.1007/BF01182789. |
[25] |
G. Papaschinopoulos, C. J. Schinas and G. Stefanidou, Two modifications of the Beverton-Holt equation, Int. J. Difference Equ., 4 (2009), 115-136. |
[26] |
Z. Pavić, J. Pečarić and I. Perić, Integral, discrete and functional variants of Jensen's inequality, J. Math. Inequal., 5 (2011), 253-264.
doi: 10.7153/jmi-05-23. |
[27] |
O. Tahvonen, Optimal harvesting of age-structured fish populations, Mar. Resour. Econ., 24 (2009), 147-169. |
[28] |
G. V. Tsvetkova, Construction of an optimal policy taking into account ecological constraints, (Russian) (Chita) in Modeling of natural systems and optimal control problems, VO "Nauka'', Novosibirsk, (1993), 65-74. |
[29] |
P.-F. Verhulst, Recherches mathématiques sur la loi d'accroissement de la population, Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Bruxelles, 18 (1845), 1-42. |
[30] |
F.-H. Wong, C.-C. Yeh and W.-C. Lian, An extension of Jensen's inequality on time scales, Adv. Dyn. Syst. Appl., 1 (2006), 113-120. |
[31] |
C. Xu, M. S. Boyce and J. D. Daley, Harvesting in seasonal environments, J. Math. Biol., 50 (2005), 663-682.
doi: 10.1007/s00285-004-0303-5. |
[32] |
X. Zhang, Z. Shuai and K. Wang, Optimal impulsive harvesting policy for single population, Nonlinear Anal. Real World Appl., 4 (2003), 639-651.
doi: 10.1016/S1468-1218(02)00084-6. |
[33] |
M. Ziolko and J. Kozlowski, Some optimization models of growth in biology, IEEE Trans. Automat. Cont., 40 (1995), 1779-1783.
doi: 10.1109/9.467682. |
show all references
References:
[1] |
L. Bai and K. Wang, A diffusive single-species model with periodic coefficients and its optimal harvesting policy, Appl. Math. Comput., 187 (2007), 873-882.
doi: 10.1016/j.amc.2006.09.007. |
[2] |
J. Barić, R. Bibi, M. Bohner, A. Nosheen and J. Pečarić, Jensen inequalities on time scales, in Monographs in Inequalities, ELEMENT, Zagreb, Volume 9, 2015. |
[3] |
L. Berezansky and E. Braverman, On impulsive Beverton-Holt difference equations and their applications, J. Differ. Equations Appl., 10 (2004), 851-868.
doi: 10.1080/10236190410001726421. |
[4] |
R. J. H. Beverton and S. J. Holt, On the Dynamics of Exploited Fish Populations, Fish & Fisheries Series, 1993.
doi: 10.1007/978-94-011-2106-4. |
[5] |
D. K. Bhattacharya and S. Begum, Bionomic equilibrium of two-species system. I, Math. Biosci., 135 (1996), 111-127.
doi: 10.1016/0025-5564(95)00170-0. |
[6] |
M. Bohner and R. Chieochan, The Beverton-Holt $q$-difference equation, J. Biol. Dyn., 7 (2013), 86-95. |
[7] |
M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser Boston, Inc., Boston, MA, 2001.
doi: 10.1007/978-1-4612-0201-1. |
[8] |
M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser Boston, Inc., Boston, MA, 2003.
doi: 10.1007/978-0-8176-8230-9. |
[9] |
M. Bohner, S. Stević and H. Warth, The Beverton-Holt difference equation, in Discrete dynamics and difference equations, World Sci. Publ., Hackensack, NJ, (2010), 189-193.
doi: 10.1142/9789814287654_0012. |
[10] |
M. Bohner and S. H. Streipert, The Beverton-Holt equation with periodic growth rate, Int. J. Math. Comput., 26 (2015), 1-10. |
[11] |
M. Bohner and S. H. Streipert, The Beverton-Holt $q$-difference equation with periodic growth rate, in Difference equations, discrete dynamical systems, and applications, Springer-Verlag, Berlin-Heidelberg-New York, 150 (2015), 3-14.
doi: 10.1007/978-3-319-24747-2_1. |
[12] |
M. Bohner and H. Warth, The Beverton-Holt dynamic equation, Appl. Anal., 86 (2007), 1007-1015.
doi: 10.1080/00036810701474140. |
[13] |
E. Braverman and L. Braverman, Optimal harvesting of diffusive models in a nonhomogeneous environment, Nonlinear Anal., 71 (2009), e2173-e2181.
doi: 10.1016/j.na.2009.04.025. |
[14] |
E. Braverman and R. Mamdani, Continuous versus pulse harvesting for population models in constant and variable environment, J. Math. Biol., 57 (2008), 413-434.
doi: 10.1007/s00285-008-0169-z. |
[15] |
C. W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources, John Wiley & Sons, Inc., New York, 1990. |
[16] |
T. Diagana, Almost automorphic solutions to a Beverton-Holt dynamic equation with survival rate, Appl. Math. Lett., 36 (2014), 19-24.
doi: 10.1016/j.aml.2014.04.011. |
[17] |
M. Fan and K. Wang, Optimal harvesting policy for single population with periodic coefficients, Math. Biosci., 152 (1998), 165-177.
doi: 10.1016/S0025-5564(98)10024-X. |
[18] |
B.-S. Goh, Management and Analysis of Biological Populations, Volume 8, Elsevier North-Holland, Inc., New York, NY, 1980. |
[19] |
M. Holden, Beverton and Holt revisited, Fisheries Research, 24 (1995), 3-8.
doi: 10.1016/0165-7836(95)00377-M. |
[20] |
W. Kelley and A. Peterson, Difference Equations: An Introduction with Applications, Academic Press, Inc., Boston, MA, 1991. |
[21] |
C. Kent, V. Kocic and Y. Kostrov, Attenuance and resonance in a periodically forced sigmoid Beverton-Holt model, Int. J. Difference Equ., 7 (2012), 35-60. |
[22] |
V. L. Kocic, A note on the nonautonomous Beverton-Holt model, J. Difference Equ. Appl., 11 (2005), 415-422.
doi: 10.1080/10236190412331335463. |
[23] |
V. L. Kocic and Y. Kostrov, Dynamics of a discontinuous discrete Beverton-Holt model, J. Difference Equ. Appl., 20 (2014), 859-874.
doi: 10.1080/10236198.2013.824968. |
[24] |
A. W. Leung, Optimal harvesting-coefficient control of steady-state prey-predator diffusive Volterra-Lotka systems, Appl. Math. Optim., 31 (1995), 219-241.
doi: 10.1007/BF01182789. |
[25] |
G. Papaschinopoulos, C. J. Schinas and G. Stefanidou, Two modifications of the Beverton-Holt equation, Int. J. Difference Equ., 4 (2009), 115-136. |
[26] |
Z. Pavić, J. Pečarić and I. Perić, Integral, discrete and functional variants of Jensen's inequality, J. Math. Inequal., 5 (2011), 253-264.
doi: 10.7153/jmi-05-23. |
[27] |
O. Tahvonen, Optimal harvesting of age-structured fish populations, Mar. Resour. Econ., 24 (2009), 147-169. |
[28] |
G. V. Tsvetkova, Construction of an optimal policy taking into account ecological constraints, (Russian) (Chita) in Modeling of natural systems and optimal control problems, VO "Nauka'', Novosibirsk, (1993), 65-74. |
[29] |
P.-F. Verhulst, Recherches mathématiques sur la loi d'accroissement de la population, Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Bruxelles, 18 (1845), 1-42. |
[30] |
F.-H. Wong, C.-C. Yeh and W.-C. Lian, An extension of Jensen's inequality on time scales, Adv. Dyn. Syst. Appl., 1 (2006), 113-120. |
[31] |
C. Xu, M. S. Boyce and J. D. Daley, Harvesting in seasonal environments, J. Math. Biol., 50 (2005), 663-682.
doi: 10.1007/s00285-004-0303-5. |
[32] |
X. Zhang, Z. Shuai and K. Wang, Optimal impulsive harvesting policy for single population, Nonlinear Anal. Real World Appl., 4 (2003), 639-651.
doi: 10.1016/S1468-1218(02)00084-6. |
[33] |
M. Ziolko and J. Kozlowski, Some optimization models of growth in biology, IEEE Trans. Automat. Cont., 40 (1995), 1779-1783.
doi: 10.1109/9.467682. |
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