Logistička funkcija u migracijama

master's thesis

• Author: Neira Hadžismajlović
• Mentor: Hrvoje Šikić (mentor)
• Committee member: Hrvoje Šikić (predsjednik povjerenstva)
• Committee member: Maja Starčević (član povjerenstva)
• Committee member: Pavle Goldstein (član povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Logistička funkcija opisana je formulom \[N(t)=\frac{K}{1+\left(\frac{K-N_0}{N_0}\right){e}^{-k_0t}}\] te je za njen logistički model značajno da stopa rasta opada. Glavninu ovog rada predstavlja logistički rast u migracijama, tj. logistički rast s konstantnom emigracijom ili imigracijom. Diferencijalna jednadžba za logistički rast s konstantnom imigracijom glasi \[\frac{dN}{dt}=aN-b{N}^{2}+s,\] pri čemu je \(s\) stopa useljavanja, dok logistički rast s konstantnom emigracijom zapisujemo \[\frac{dN}{dt}=aN-b{N}^{2}-h\] pri čemu je \(h\) stopa iseljavanja. Kroz različite primjere i grafove uočavamo logistički rast.

Abstract (english)

The logistic function is described by the formula \[N(t)=\frac{K}{1+\left(\frac{K-N_0}{N_0}\right){e}^{-k_0t}}\] and for its logistic model it is significant that the rate of growth declines. The main goal of this work is to present logistic growth in migration - logistics growth with constant emigration or immigration. The differential equation for logistic growth with constant imigration is \[\frac{dN}{dt}=aN-b{N}^{2}+s,\] where \(s\) is the immigration rate, while logistical growth with constant emigration we write \[\frac{dN}{dt}=aN-b{N}^{2}-h\] where \(h\) is the harvesting rate. Through various examples and graphs, we see a logistic growth.

• Keywords: logistička funkcija; migracije; emigracija; imigracija
• Keywords (english): logistic function; migration; emigration; immigration
• Language: croatian
• URN:NBN: urn:nbn:hr:217:737700
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-04-23 11:57:10