Abstract
For a model describing the dynamics of two competing size-structured populations under chosen intensities of their exploitation, the existence and uniqueness of a stationary solution is proved. It is shown that there exist exploitation intensities that maximize a given profit functional on the stationary solution corresponding to them.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. F. Murphy, “A nonlinear growth mechanism in size structured population dynamics,” J. Theor. Biol. 104, 493–506 (1983).
A.M. Roos, “A gentle introduction to models of physiologically structured populations,” in Structured-Population Models in Marine, Terrestrial, and Freshwater Systems, Ed. by S. Tuljapurkar and H. Caswell (Chapman and Hall, New York, 1997), Ser. Population and Community Biology, Vol. 18, pp. 119–204.
A. A. Panesh and A. S. Platov, “Optimization of size-structured population with interacting species,” J. Math. Sci. 188(3), 293–298 (2013).
A. A. Davydov and A. S. Platov, “Optimal stationary solution in forest management model by accounting intra-species competition,” Moscow Math. J. 12(2), 269–273 (2012).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Nauka, Moscow, 1976; Dover, New York, 1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.A. Davydov, A.S. Platov, 2013, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Vol. 19, No. 4.
Rights and permissions
About this article
Cite this article
Davydov, A.A., Platov, A.S. Optimal exploitation of two competing size-structured populations. Proc. Steklov Inst. Math. 287 (Suppl 1), 49–54 (2014). https://doi.org/10.1134/S0081543814090053
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543814090053