Use of Lotka-Volterra differential equations for the creation of the model of combat use of military formation in the mutual fire conditions
DOI:
https://doi.org/10.33577/2312-4458.23.2020.27-33Keywords:
military formation capabilities, fire for effect of the enemy, differential equations of Lotka-VolterraAbstract
The analysis of armed conflicts of recent decades suggests that the quantitative advantage in forces and means does not always ensure the successful completion of combat missions. Quite often, the organization of military formations combat use and enemy fire demage comes to the fore from the whole set of factors.
The article considers the possibility of using Lotka-Voltair differential equations in creating a model of combat use of military formations in terms of fire interaction.
These equations are widely used in the study of population growth dynamics of biological species under conditions of competition (when both parties are predators). The main hypotheses when using the above equations include the following: the supplies needed for growth are either available in unlimited quantities, or their income is strictly regulated over time; species harm each other, and per unit time the number of losses is always proportional to the probability of encountering individuals of these two species.
The application of the Lotka-Voltair equations allows to determine the dynamics of changes in the level of military formation capabilities in the conditions of mutual fire influence of the parties and to determine the critical level of capabilities, and further, on the basis of this information to provide recommendations for changing certain constants.
References
Repilo YU.YE. (2001), "Vohneve urazhennya protyvnyka i boyove zabezpechennya pry boyovykh diyakh u lokalʹnymu konflikti v umovakh hirsʹko-lisystoyi mistsevosti." [Enemy fire defeat and combat support during fighting in local conflict under mountainous and forest terrain conditions]: Tutorial, NAOU, Kyiv, 56 p. [in Ukrainian].
Maystrenko O.V. (2016), "Udoskonalennya zmistu pryntsypiv zastosuvannya raketnykh viysʹk i artylerii pid chas vohnevoho urazhennya protyvnyka." [The content of principles improving of missile troops and artillery using during enemy fire] Collection of scientific works of the Center for Military and Strategic Studies of the Ivan Chernoyakhovsky National University of Defense of Ukraine. Kyiv, 2016. Issue № 3 (58). pp. 75–80. DOI: https://doi.org/10.33099/2304-2745/2016-3-58/75-80. (Accessed 29 May 2020). [in Ukrainian].
Adamchuk M.M, Norchuk YU.V., Luhovsʹkyy I.S. and Mynʹko O.V. (2019), " Analiz sposobiv zastosuvannya artyleriyi v zbroynykh konfliktakh." [Ways analysis of artillery use in armed conflicts] Collection of scientific works. Odessa, 2019. Issue № 1 (11). pp. 155-163. DOI: https://doi.org/10.37129/2313-7509.2019.11.155-163 (Accessed 16 June 2020). [in Ukrainian].
Shulgin V.E., and Fesenko Yu.N. (1997), " O kriteriyakh ognevogo porazheniya ob’yektov i gruppirovok voysk v operatsii." [On the criteria for fire destruction of objects and groupings of troops in operations]. Military thought. Moscow, 1997. Issue No 6. pp. 58-64.
URL: http://militaryarticle.ru/voennaya-mysl/1997-vm/9656-o-kriterijah-ognevogo-porazhenija-obektov-i. (Accessed 26 May 2020). [in Ukrainian].
Kalinovskiy O.N. (1996), "Ob otsenke ognevykh vozmozhnostey voysk v operatsii." [On the assessment of fire capabilities of troops in operations]. Military thought. Moscow, 1996. Issue No 5. pp. 52–56. URL: http://militaryarticle.ru/ voennaya-mysl/1996-vm/8805-ob-ocenke-ognevyh-vozmozhnostej- vojsk-v-operacii . (Accessed 26 May 2020). [in Ukrainian].
Trotsenko K.A. (2008), "O realizatsii boyevykh vozmozhnostey takticheskoy gruppirovki voysk." [On the implementation of combat capabilities of the tactical grouping of troops]. Military Thought. Moscow, 2008. Issue No 6. pp. 70–75. URL:http://militaryarticle.ru/voennaya-mysl/2008-vm/10159-o-realizacii-boevyh-vozmozhnostej-takticheskoj. (Accessed 27 May 2020). [in Ukrainian].
Buyanov B.B., Lubkov N.V. and Polyak G.L. (2007), "Matematicheskaya model' dlitel'nogo vooruzhennogo konflikta" [Mathematical model of long-term armed conflict]. Management problems. Moscow, 2007. Issue No 5. pp. 48-51. URL: https://cyberleninka.ru/article/n/matematicheskaya-model-dlitelnogo-vooruzhennogo-konflikta/viewer. (Accessed 26 May 2020). [in Ukrainian].
Polyak G.L. (2011), "Matematicheskaya model' ekonomicheskikh posledstviy vooruzhennogo protivostoyaniya neravnykh po sile protivnikov." [A mathematical model of the economic consequences of armed confrontation with unequal opponents]. Mathematical and instrumental methods of economics. Tambov, 2011. Issue No 12 (85). pp. 381–386. URL: http://ecsocman.hse.ru/data/2012/10/03/1251351717/ 81.pdf. (Accessed 27 May 2020). [in Ukrainian].
Polenin V.I. (2004), " Primeneniye veroyatnostnykh modeley pri planirovanii operatsiy " [Application of probabilistic models in operations planning]. Military Thought. Moscow. 2004. Issue No 3. pp. 54-55. URL: http:// militaryarticle.ru/voennaya-mysl/2004-vm/9430-primenenie-verojatnostnyh-modelej-pri-planirovanii. (Accessed 28 May 2020). [in Ukrainian].
Bondarchuk S.S. and Perevozkin V.P. (2014), "Matematicheskoye modelirovaniye v populyatsionnoy ekologii” [Mathematical modeling in population ecology]: Tutorial, TGPU, Tomsk 224 p. [in Ukrainian].
Maistrenko O.V., Karavanov O.A., Stegura S.I., Davidovsky L.S., and Spasun V.I.(2020) "Doslidzhennya funktsionuvannya rozviduvalʹno-vohnevoyi systemy shlyakhom stvorennya modeli vohnevoho urazhennya protyvnyka." [Reconnaissance fire system functioning research by creating a model of enemy fire destruction.]. Weapons and military equipment. Kyiv, 2020.. Issue № 2 (26). pp. 50-58. [in Ukrainian]. DOI: https://doi.org/10.34169/2414-0651. 2020.2 (26).50-58.
Uhm, H., Lee, Y..(2019) , "A Heuristic Algorithm for Weapon Target Assignment and Scheduling." [ A Heuristic Algorithm for Weapon Target Assignment and Scheduling]. Military Operations Research. 2019. Issue № 24(4). pp. 53-62. DOI:http://doi.org/10.5711/1082598324453. (Accessed 28 May 2020). [in Ukrainian].
Maistrenko O.V., Repilo YU.YE. and Demidko D.L. (2015), "Vyznachennya oblasti dotsilʹnykh znachenʹ dlya pokaznykiv tochnosti ta raptovosti vohnyu artylerii (udariv raket)." [Determination of appropriate values range for indicators of accuracy and suddenness of artillery fire (missile strikes)]. Modern information technologies in the field of security and defense. Kyiv, 2015. Issue № 1 (22). pp. 79–83. URL: http://nbuv.gov.ua/UJRN/sitsbo_2015_1_15. (Accessed 28 May 2020). [in Ukrainian].
