Problems of «Predator–Prey» Model Use in Economic Practice

TitleProblems of «Predator–Prey» Model Use in Economic Practice
Publication TypeJournal Article
Year of Publication2011
AuthorsKozik, VV, Sidorov, Yu.I
Short TitleNauka innov.
DOI10.15407/scin7.01.005
Volume7
Issue1
SectionScientific Basis of Innovation Activity
Pagination5-15
LanguageUkrainian
Abstract
Reasons of classic and the modified models of «predator–prey» type are not disseminated among practical economists are considered. They are — essential simplification of classic model and complication of the modified discrete models, their large variety, that does not allow adequate choosing of concrete model, describing and forecasting the behaviour of the real economic systems, elements of which have difficult mutual relations. Simulation computer design is a perspective prognostic method of analysis of economic situations on the base of various models. Thus the model of «predator–prey» can find a deserving place in a number of rules-routines by which a computer model is created.
Keywordscomputer simulation of economic problems, forecasting, «predator–prey» model
References
1. Vol'terra V. Matematicheskaja teorija bor'by za sushhestvovanie (Theorie mathematique de la lutter pour la vie, 1931) per. s franc. pod red. Ju.M. Svirezheva. Moskva: Nauka, 1976 [in Russian].
2. Riznichenko G.Ju. Lekcii po matematicheskim modeljam v biologii. Chast' I. Izhevsk: NIC Reguljarnaja i haoticheskaja dinamika, 2002 [in Russian].
3. Burakov Ju.G., Sokolov V.A. Obobshhenie rezul'tatov modelirovanija raboty sistemy ciklicheskogo gazlifta v rezhime vynuzhdennyh kolebanij. Neftegazovoe delo. 2005. T. 3: 105-117 [in Russian].
4. Romanovskij M.Ju., Romanovskij Ju.M. Vvedenie v jekonofiziku. Statisticheskie i dinamicheskie modeli. Moskva-Izhevsk: Institut komp'juternyh issledovanij, 2007 [in Russian].
5. Vasil'eva E.A., Andreev V.V. Modelirovanie dinamiki social'no-jekonomicheskoj sistemy Rossii. Matematika, komp'juter, obrazovanie. http://www.mce.su/rus/sessions/S4/ (2009) [in Russian].
6. Andreev V.V., Karpova O.V. Issledovanie devjati jelementnoj matematicheskoj modeli social'no-jekonomicheskoj sistemy. Matematika, komp'juter, obrazovanie. http://www.mce.su/rus/sessions/S4/ (2009) [in Russian].
7. Andreev V.V., Andreeva E.V., Burmistrova L.A. Modelirovanie i issledovanie dinamiki vzaimodejstvija slozhnyh konkurirujushhih sistem. http://www.mce.su/rus/sessions/S4/ (2009) [in Russian].
8. Macenko A.M. Jekologo-jekonomicheskie principy modelirovanija ciklicheskih kolebanij v jekonomike. Visnik SumDU. Serija Ekonomika. 2007. No 1: 103-110 [in Russian].
9. Zang V.-B. Sinergeticheskaja jekonomika. Moskva: Mir, 1999 [in Russian].
10. Balackij E.V., Ekimova N.A. Konkurencija i privatizacionnyj cikl: vzaimnoe vlijanie i mehanizm soprjazhenija. http://www.kapital-rus.ru/articles/article/175799 [in Russian].
11. Balackij E.V. Modelirovanie processov mezhsektoral'noj konkurencii. Obshhestvo i jekonomika. 2008. No 5: 54-70 [in Russian].
12. Kaljuzhnyj D. Mirovedenie XXI. Proekt «HRONOTRON». http://hronotron.narod.ru/hronotronika/part3.txt [in Russian].
13. Gercekovich D.A. Zerkal'nye pary. Algoritm «Linza». Izvestija IGJeA. 2007, 54(4): 35-38 [in Russian].
14. Zimina M.V. Matematicheskaja model' jevoljucii i vzaimodejstvija populjacij. Informacionnye tehnologii i programmirovanie: Mezhvuzovskij sbornik statej. Vyp.1 (6):5-18 [in Russian].
15. Lebedeva E.V. Modifikacija matematicheskoj modeli «zhishhnik—zhertva» v sociologii, uchityvajushhaja predstavitelej nejtral'noj proslojki obshhestva. Trudy Nauchnoj konferencii po radiofizike. N.-Novgorod: NNGU, 2001. S. 323-324 [in Russian].
16. Vot — odna iz svjashhennyh tajn sovremennosti-17. http://politiko.com.ua/blogpost8994 [in Russian].
17. Mari Dzh. Nelinejnye differencial'nye uravnenija v biologii. Lekcii o modeljah: Per. s angl. Moskva: Mir, 1983 [in Russian].
18. Gause G.F. The struggle for existence. Baltimore: Williams and Wilkins, 1934. (Pereizdanie: New York: Dover, 1971); Gauze G.F Bor'ba za sushhestvovanie. Internet, jelektronnaja versija (http://www.ggause.com/titpagru.htm). Glava 6. http://www.ggause.com/gaurus06.htm
19. Gilpin M.E. Do hares eat lynx? Amer. Naturalist. 1973, 107(957): 727-730.
https://doi.org/10.1086/282870
20. Cit. po: Rozenberg G.S., Rjanskij F.N. Teoreticheskaja i prikladnaja jekologija: Uchebnoe posobie. 2-e izd. Nizhnevartovsk: Izd-vo Nizhnevart. ped. inta, 2005 [in Russian].
21. Malineckij G.G., Kurdjumov S.P. Nelinejnaja dinamika i problemy prognoza. Vestnik RAN. 2001, 71(3): 210-213 [in Russian].
22. Verhulst P.F. Recherches Mathematiques sur La Loi D’Accroissement de la Population. Nouveaux Memoires de l’Academie Royale des Sciences et Belles-Lettres de Bruxelles. 1845. 18, Art. 1. P. 1-45.
23. Bazykin A.D. Matematicheskaja biofizika vzaimodejstvujushhih populjacij. Moskva: Nauka, 1985 [in Russian].
24. Sydorov Ju.I. Vykorystannja rivnjannja Mono dlja iteracijnogo rozrahunku periodychnyh procesiv fermentacii'. Biotehnologija. 2010, 3(1): 56-60 [in Ukrainian].
25. Sydorov Ju.I., Kozyk V.V. Zastosuvannja rivnjannja Mono dlja opysu dynamiky pojavy innovacij. Aktual'ni problemy ekonomiky. 2010. No 3: 268-274 [in Ukrainian].
26. Kolesov Ju.S. Matematicheskie modeli jekologii. Issledovanija po ustojchivosti i teorii kolebanij. Jaroslavl': Izd-vo JarGU, 1979 [in Russian].
27. Muzychuk O.V. Verojatnostnye harakteristiki sistemy «hishhnik—zhertva» so sluchajno izmenjajushhimisja parametrami. Izv. vuzov. Prikladnaja nelinejnaja dinamika. 1997, 5(2): 80-86 [in Russian].
28. Gardiner K.V. Stohasticheskie metody v estestvennyh naukah. Moskva: Mir, 1986 [in Russian].
29. Ayala F.G., Gilpin M.E., Ehrenfeld J.G. Competition between species: theoretical models and experimental tests. Theoret. popul. biol. 1974, 4(3): 331-356.
https://doi.org/10.1016/0040-5809(73)90014-2
30. Kipjatkov V.E. Praktikum po matematicheskomu modelirovaniju v populjacionnoj jekologii (uchebnoe posobie). Sankt-Peterburg: S.-Peterb. gos. un-t, 2002 [in Russian].
31. Holling C.S. Some characteristics of simple types of predation and parasitism. Canadian Entomologist. 1959. V. 91. P. 385-398.
https://doi.org/10.4039/Ent91385-7
32. Tanner J.T. The stability and the in trinsic growth rates of prey and predator populations. Ecology. 1975. V. 56. P. 855-867.
https://doi.org/10.2307/1936296
33. Kolmogorov A.N. Kachestvennoe izuchenie matematicheskih modelej dinamiki populjacij. Problemy kibernetiki. 1972. Vyp. 25. S. 100-106 [in Russian].
34. Rosenzweig M.L., MacArthur R.H. Graphycal representation and stability conditions of predator- prey interactions. Amer. Natur. 1963. V. 97. P. 209-223.
https://doi.org/10.1086/282272
35. Zul'pukarov M.-G.M., Malineckij G.G., Podlazov A.V. Metod rusel i dzhokerov na primere issledovanija sistemy Rozencvejga-Makartura (2006). http://www.keldysh.ru/papers/2006/prep21 [in Russian].
36. Bazykin A.D. Nelinejnaja dinamika vzaimodejstvujushhih populjacij. Moskva: Institut komp'juternyh issledovanij, 2003 [in Russian].
37. Belyh V.N. Jelementarnoe vvedenie v kachestvennuju teoriju i teoriju bifurkacij dinamicheskih sistem. Sorovskij obrazovatel'nyj zhurnal. 1997. No 1: 115-121 [in Russian].
38. Bljumin S.L., Shmyrin A.M. Okrestnostnye sistemy. Lipeck: Lipeckij jekologo-gumanitarnyj institut, 2005 [in Russian].
39. Zajcev V.V., Karlov-mladshij A.V., Telegin S.S. DV-model' sistemy «hishhnik-zhertva». Vestnik SamGU — Estestvennonauchnaja serija. 2009, 72(6): 139-148 [in Russian].
40. Gostev A. Ekonomika namerenij. http://www.dmdays.com.ua/biblioteka/256.html [in Russian].
41. Kozyk V.V., Sydorov Ju.I., Skvorcov I.B., Tarasovs'ka O.B. Zastosuvannja modeli Lotki-Vol'terra dlja opysu duopol'no-duopsonijevoi' konkurencii'. Aktual'ni problemy ekonomiky. 2010. No 2(104): 252-260 [in Ukrainian].
42. Tarasovs'ka O.B., Kozyk V.V., Sydorov Ju.I. Prognozuvannja vnutrishn'ofirmovoi' tovarnoi' konkurencii'. Ekonomika: problemy teorii' ta praktyky. 2009. T. IX, vypusk 255. S. 2307-2311 [in Ukrainian].
43. Bort Dzh. Prikosnovenie carja Midasa. http://www.osp.ru/cw/1996/23/12375 [in Russian].
44. Nikol'skij S.O. Modelirovanie ocenki harakteristik nadezhnosti bankovskih tirazhnyh programm sistem na osnove nejrosetevyh tehnologij. Avtoreferat kand. dis. Brjansk: GOUVPO «Brjanskij gosudarstvennyj tehnicheskij universitet», 2006 [in Russian].
45. Silverberg G. Evolutionary Modeling in Economics: Recent History and Immediate Prospects. Prepared for the workshop on «Evolutionary Economics as a Scientific Research Programme», Stockholm, May 26-27, 1997. 17 p. http://www.merit.unu.edu/publications/rmpdf/1997/rm1997-013.pdf
46. Cisar' I.F., Nejman V.G. Komp'juternoe modelirovanie ekonomiki. Moskva: Dialog-MIFI, 2008 [in Russian].
47. Scholz R., Pyka A. A Schumpeterian Model of Energy Markets. 2009. V. 40 (5). P. 418-440.