On Estimation of an Average Time Profit in Probabilistic Environmental and Economic Models
We consider environmental-economical models of optimal harvesting, given by the differential equations with impulse action, which depend on random parameters. We assume, that lengths of intervals θk between the moments of impulses τk are random variables and the sizes of impulse influence depend on...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Yaroslavl State University
2018-06-01
|
| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/685 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1839573278505566208 |
|---|---|
| author | Lyudmila I. Rodina Ilya I. Tyuteev |
| author_facet | Lyudmila I. Rodina Ilya I. Tyuteev |
| author_sort | Lyudmila I. Rodina |
| collection | DOAJ |
| description | We consider environmental-economical models of optimal harvesting, given by the differential equations with impulse action, which depend on random parameters. We assume, that lengths of intervals θk between the moments of impulses τk are random variables and the sizes of impulse influence depend on random parameters vk, k = 1, 2, . . . One example of such objects is an equation with impulses, modelling dynamics of the population subject to harvesting. In the absence of harvesting, the population development is described by the differential equation ˙x = g(x) and in time moments τk some random share of resource vk, k = 1, 2, . . . is taken from population. We can control gathering process so that to stop harvesting when its share will appear big enough to keep possible biggest the rest of a resource to increase the size of the following gathering. Let the equation ˙x = g(x) have an asymptotic stable solution ϕ(t) ≡ K and the interval (K1, K2) is the attraction area of the given solution (here 0 ≤ K1 < K < K2). We construct the control u = (u1, . . . , uk, . . .), limiting a share of harvesting resource at each moment of time τk, so that the quantity of the remained resource, since some moment τk0 , would be not less than the given value x ∈ (K1, K). For any x ∈ (K1, K) the estimations of average time profit, valid with probability one, are received. It is shown, that there is a unique x∗ ∈ (K1, K), at which the lower estimation reaches the greatest value. Thus, we described the way of population control at which the value of average time profit can be lower estimated with probability 1 by the greatest number whenever possible. |
| format | Article |
| id | doaj-art-bb76f2c0bbd540e3b1a8bda80c48cd6c |
| institution | Matheson Library |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2018-06-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-bb76f2c0bbd540e3b1a8bda80c48cd6c2025-08-04T14:06:38ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172018-06-0125325726710.18255/1818-1015-2018-3-257-267504On Estimation of an Average Time Profit in Probabilistic Environmental and Economic ModelsLyudmila I. Rodina0Ilya I. Tyuteev1Vladimir State University named after Alexander and Nikolay StoletovsUdmurt State UniversityWe consider environmental-economical models of optimal harvesting, given by the differential equations with impulse action, which depend on random parameters. We assume, that lengths of intervals θk between the moments of impulses τk are random variables and the sizes of impulse influence depend on random parameters vk, k = 1, 2, . . . One example of such objects is an equation with impulses, modelling dynamics of the population subject to harvesting. In the absence of harvesting, the population development is described by the differential equation ˙x = g(x) and in time moments τk some random share of resource vk, k = 1, 2, . . . is taken from population. We can control gathering process so that to stop harvesting when its share will appear big enough to keep possible biggest the rest of a resource to increase the size of the following gathering. Let the equation ˙x = g(x) have an asymptotic stable solution ϕ(t) ≡ K and the interval (K1, K2) is the attraction area of the given solution (here 0 ≤ K1 < K < K2). We construct the control u = (u1, . . . , uk, . . .), limiting a share of harvesting resource at each moment of time τk, so that the quantity of the remained resource, since some moment τk0 , would be not less than the given value x ∈ (K1, K). For any x ∈ (K1, K) the estimations of average time profit, valid with probability one, are received. It is shown, that there is a unique x∗ ∈ (K1, K), at which the lower estimation reaches the greatest value. Thus, we described the way of population control at which the value of average time profit can be lower estimated with probability 1 by the greatest number whenever possible.https://www.mais-journal.ru/jour/article/view/685model of a population subject to harvestingaverage time profitoptimal exploitation |
| spellingShingle | Lyudmila I. Rodina Ilya I. Tyuteev On Estimation of an Average Time Profit in Probabilistic Environmental and Economic Models Моделирование и анализ информационных систем model of a population subject to harvesting average time profit optimal exploitation |
| title | On Estimation of an Average Time Profit in Probabilistic Environmental and Economic Models |
| title_full | On Estimation of an Average Time Profit in Probabilistic Environmental and Economic Models |
| title_fullStr | On Estimation of an Average Time Profit in Probabilistic Environmental and Economic Models |
| title_full_unstemmed | On Estimation of an Average Time Profit in Probabilistic Environmental and Economic Models |
| title_short | On Estimation of an Average Time Profit in Probabilistic Environmental and Economic Models |
| title_sort | on estimation of an average time profit in probabilistic environmental and economic models |
| topic | model of a population subject to harvesting average time profit optimal exploitation |
| url | https://www.mais-journal.ru/jour/article/view/685 |
| work_keys_str_mv | AT lyudmilairodina onestimationofanaveragetimeprofitinprobabilisticenvironmentalandeconomicmodels AT ilyaityuteev onestimationofanaveragetimeprofitinprobabilisticenvironmentalandeconomicmodels |