For citation:
Trubetskov D. I. Phenomenon of Lotka–Volterra mathematical model and similar models. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 2, pp. 69-88. DOI: 10.18500/0869-6632-2011-19-2-69-88
Phenomenon of Lotka–Volterra mathematical model and similar models
Lotka–Volterra mathematical model (often called «predator–prey» model) is applicable for different processes description in biology, ecology, medicine, in sociology investigations, in history, radiophysics, ets. Variants of this model is considered methodologicaly in this review. The next models are observed: model of contamination or other dirty interaction with surroundigs; model of class struggle; model of classless society – epock of huntersgatherers; military operations model; model of virus infection diseases; model of epidemic spreading, so virus of computers infection spreading; model of cognitive and(or) emotion cerebral modes.
- Darwin C. Autobiography. London: St. James’s Place; 1958. P. 120.
- Browne J. Darwin’s Origin of Species. Atlantic Montly Press; 2007. 174 p.
- Malthus TR. An assay on the principle of population, as it affects the future improvement of society. 1798. Available from: http://www.faculty.rsu.edu/felwell/Theorists/Malthus/essay2.htm.
- Lotka A. Elements of Physical Biology. Baltimore; 1925. Reprinted by Dover in 1956 as Elements of Mathematical Biology. 460 p.
- Volterra V. Mathematical Theory of the Struggle for Existence. Moscow: Fizmatlit; 1976. 288 p. (in Russian).
- Bratus AS, Novozhilov AS, Platonov AP. Dynamical Systems and Models of Biology. Moscow: Fizmatlit; 2010. 400 p. (in Russian).
- Bazykin AD. Nonlinear Dynamics of Interacting Populations. World Scientific; 1998. 216 p. DOI: 1142/2284.
- Arnold VI. "Hard" and "soft" models. Nature. 1998;(4):3 (in Russian).
- Bratus AS, Meshcherin AS, Novozhilov AS. Mathematical models of the interaction of pollution with the environment. Moscow University Computational Mathematics and Cybernetics. 2001;6:140 (in Russian).
- Zhang WB. Synergetic Economics. Time and Change in Nonlinear Economics. Berlin: Springer; 1991. 246 p. DOI: 10.1007/978-3-642-75909-3.
- Goodwin RM. A Growth Model. Socialism and Growth. Cambridge: University Press; 1967.
- Malkov SY. Social Self-Organization and the Historical Process. Moscow: URSS; 2009. 372 p. (in Russian).
- Lanchester FW. Aircraft in Warfire: The Down of the Fourth Arm. London: Constable; 1916. 243 p.
- Osipov MO. On the influence of the number of forces entering the battle on their losses. War Collection, June-October, 1915 (in Russian).
- Bell G. Predator—prey equations simulating on immune response. Math. Biosci. 1973;16(3–4):291–314. 10.1016/0025-5564(73)90036-9.
- Marchuk GI. Mathematical Models in Immunology and Medicine. Ch.2. Moscow: Nauka; 1985. 239 p. (in Russian)
- Kermack WO, McKendrick AG. Contribution to the mathematical theory of epidemics. Proceedings of Royal Statistical Society A. 1927;115(772):700–721. DOI: 10.1098/rspa.1927.0118.
- Rabinovich MI, Muezzinoglu MK. Nonlinear dynamics of the brain: emotion and cognition. Phys. Usp. 2010;53(4):357–372. DOI: 10.3367/UFNe.0180.201004b.0371.
- Neimark YI. Mathematical Models in Natural Science and Engineering. Berlin: Springer; 2003. 572 p. DOI: 10.1007/978-3-540-47878-2.
- 3480 reads