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Smooth Models of Biological Populations
Author(s) -
E.V. Lobanova,
N.B. Medvedeva
Publication year - 2014
Publication title -
bulletin of the south ural state university series mathematical modelling programming and computer software
Language(s) - Uncategorized
Resource type - Journals
eISSN - 2308-0256
pISSN - 2071-0216
DOI - 10.14529/mmp140205
Subject(s) - geography , evolutionary biology , biology
Ïðåäëîæåí ìåòîä ïîñòðîåíèÿ ìîäåëåé, âûðàæàþùèõ ÷èñëåííîñòü áèîëîãè÷åñêèõ ïîïóëÿöèé, íà îñíîâå âðåìåííûõ ðÿäîâ. Íà ïåðâîì ýòàïå ñòðîèòñÿ ñãëàæåííûé íàáîð ýìïèðè÷åñêèõ äàííûõ, êîòîðûé îòðàæàåò îáùèå ÷åðòû ðåàëüíîãî âðåìåííîãî ðÿäà. Ýòî äîñòèãàåòñÿ ïîñðåäñòâîì ïîñòðîåíèÿ îïòèìèçàöèîííîãî ñïëàéíà êóñî÷íîïîëèíîìèàëüíîé ôóíêöèè, èìåþùåé ìèíèìàëüíîå îòêëîíåíèå îò ýìïèðè÷åñêèõ äàííûõ ïî ìåòîäó íàèìåíüøèõ êâàäðàòîâ. Äàëåå ñòðîèòñÿ ñèñòåìà äèôôåðåíöèàëüíûõ óðàâíåíèé, ïðàâàÿ ÷àñòü êîòîðîé èìååò íàèìåíüøåå îòêëîíåíèå ïî ìåòîäó íàèìåíüøèõ êâàäðàòîâ îò ïðîèçâîäíîé îïòèìèçàöèîííîãî ñïëàéíà íà íåêîòîðîé áîëåå ÷àñòîé ñåòêå. Ðåøåíèå çàäà÷è Êîøè äëÿ ïîñòðîåííîé ñèñòåìû íà òåñòîâîì ïðîìåæóòêå âðåìåíè áåðåòñÿ â êà÷åñòâå ïðîãíîçà ìîäåëè. Ìåòîä ïðèìåíÿåòñÿ ê êîíêðåòíûì âðåìåííûì ðÿäàì, äåëàåòñÿ îöåíêà ïîãðåøíîñòè ïðîãíîçà, èññëåäóåòñÿ çàâèñèìîñòü ïîãðåøíîñòè îò ïàðàìåòðîâ ìåòîäà. Êðîìå òîãî ìåòîä ïðèìåíÿåòñÿ ê èñêóññòâåííîìó âðåìåííîìó ðÿäó, ñîäåðæàùåìó ñëó÷àéíûå âîçìóùåíèÿ. Èññëåäóåòñÿ çàâèñèìîñòü ïîãðåøíîñòè ïðîãíîçà îò âåëè÷èíû âîçìóùåíèÿ. Êëþ÷åâûå ñëîâà: âðåìåííîé ðÿä; ìîäåëü ïîïóëÿöèè; ñïëàéí; ìåòîä íàèìåíüøèõ êâàäðàòîâ.

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