Co możemy opisać układem dynamicznym?
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2014)
- Volume: 6, page 73-85
- ISSN: 2080-9751
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topUrszula Foryś. "Co możemy opisać układem dynamicznym?." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 6 (2014): 73-85. <http://eudml.org/doc/296314>.
@article{UrszulaForyś2014,
abstract = {In this paper we present several examples of simple dynamical systemsdescribing various real processes. We start from well know Fibonaccisequence, through Lotka-Volterra model of prey-predator system, love affairdynamics, ending with modelling of tumour growth.},
author = {Urszula Foryś},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
keywords = {dynamical system; mathematical modelling; discrete model; continuous model; stability; eigenvalue},
language = {pol},
pages = {73-85},
title = {Co możemy opisać układem dynamicznym?},
url = {http://eudml.org/doc/296314},
volume = {6},
year = {2014},
}
TY - JOUR
AU - Urszula Foryś
TI - Co możemy opisać układem dynamicznym?
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2014
VL - 6
SP - 73
EP - 85
AB - In this paper we present several examples of simple dynamical systemsdescribing various real processes. We start from well know Fibonaccisequence, through Lotka-Volterra model of prey-predator system, love affairdynamics, ending with modelling of tumour growth.
LA - pol
KW - dynamical system; mathematical modelling; discrete model; continuous model; stability; eigenvalue
UR - http://eudml.org/doc/296314
ER -
References
top- Bartłomiejczyk, A. (red.): 2013, Metody matematyczne w zastosowaniach. Tom 1, Centrum Zastosowań Matematyki, Politechnika Gdańska, Gdańsk.
- Bodnar, M.: 2013, Zbiór zadań z matematyki dla biologów, Wydanie 2, Wydawnictwa Uniwersytetu Warszawskiego, Warszawa.
- Bodnar, M.: 2014, Matematyka małżeństwa, Delta 8, 9-11.
- Corbalan, F.: 2012, Złota proporcja. Matematyczny język piękna, RBA Coleccionables, Barcelona.
- Foryś, U.: 2005, Matematyka w biologii, WNT, Warszawa.
- Foryś, U., Matejek, P.: 2014, O pewnym ciekawym zastosowaniu modelu drapieżnik--ofiara, Delta 8, 12-15.
- Gompertz, G.: 1825, On the nature of the function expressive of the law of human mortality, and on the new mode of determining the value of life contingencies, Philos. Trans. R. Soc. 115, 513-585.
- Gotmann, J. M., Murray, J. D., Swanson, C. C., Tyson, R., Swanson, K. R.: 2002, The mathematics of marriage: dynamic nonlinear models, MIT Press, Cambridge.
- Hahnfeldt, P., Panigrahy, D., Folkman, J., Hlatky, L.: 1999, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Res. 59, 4770-4775.
- Laird, A. K.: 1964, Dynamics of tumour growth, Br. J. Cancer 18, 490-502.
- Laird, A. K.: 1965, Dynamics of tumour growth: comparison of growth rates and extrapolation of growth curve to one cell, Br. J. Cancer 19, 278-291.
- Murray, J. D.: 2002, Mathematical Biology I: An Introduction, Third Edition, Springer, Berlin.
- Murray, J. D.: 2003, Mathematical Biology II: Spatial Models and Biomedical Applications, Third Edition, Springer, Berlin.
- Murray, J. D.: 2006, Wprowadzenie do biomatematyki, Wydawnictwo Naukowe PWN, Warszawa.
- Rinaldi, S., Della Rossa, F., Dercole, F.: 2010, Love and appeal in standard couples, International Journal of Bifurcation and Chaos 20(8), 2443-2451.
- Rinaldi, S., Landi, P., Della Rossa, F.: 2013, Small discoveries can have great consequences in love affairs: The case of beauty and beast, International Journal of Bifurcation and Chaos 23(11), 1330038.
- Rudnicki, R.: 2014, Modele i metody biologii matematycznej, Część I: modele deterministyczne, Instytut Matematyczny PAN, Warszawa.
- Strogatz, S.: 1988, Love affairs and differential equations, Math. Magazine 65, 35.
- Wrzosek, D.: 2010, Matematyka dla biologów, Wydawnictwa Uniwersytetu Warszawskiego, Warszawa.
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