Understanding of the main mathematical tools, local and global, analytical and geometrical, necessary for the study of mechanical and biological models based upon equations and systems of ordinary differential equations.
Understanding of the main evolutionary models of one or more interacting populations, both in a discrete and continuous setting. Understanding of physical, medical and neurological models.
Discrete mathematical models of population growth. Equilibria and their stability. Models with continuous time. Other malthusian or logistic models. Models with delay and stability of equilibria. Interacting populations. Intra- and inter- specific competition. Extinction of species. Competition and cooperation.
The course includes various numerical simulations of the models we consider, which will be included into 12 extra laboratory lectures.
Some extra one-hour lectures complementing the topics of the course could be available, held by external teachers.
| Author | Title | Publisher | Year | ISBN | Note |
| M. Squassina, S. Zuccher | Introduzione all'Analisi Qualitativa delle Equazioni Differenziali Ordinarie. 332 pagine, 365 figure. | Apogeo Editore | 2008 | 9788850310845 | testo adottato |
| J. Murray | Mathematical Biology | Springer | 2002 | 0-387-95223-3 | testo segnalato |
| G. Gaeta | Modelli Matematici in Biologia | Springer | 2007 | 978-0-7923 | testo adottato |
Final oral examination.
M. Squassina, S. Zuccher, Introduzione all'Analisi Qualitativa delle Equazioni Differenziali Ordinarie. 332 pp, 365 fig.
(pdf, it, 8940 KB, 02/08/08)
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