Last updated: 01.10.2005.

Zlatinka I. Dimitrova and Nikolay K. Vitanov

Population dynamics and its unexpected applications

(Resume)

                The modeling of the behavior of the animal populations leads to interesting mathematical problems with unexpected additional applications. The history of the population dynamics is closely connected not only to the investigation of the animal populations but also to the wars and other disasters caused by the human action. Vito Volterra developed the system of model equations for the nonlinear dynamics of a system of competing populations. The growth rates and competition coefficients in these equations can depend on the number of the individuals of the populations. Thus the populations can adapt their behavior and chaos of Shilnikov kind can be observed. The chaotic behavior is closely connected to the phenomenon pairwise competition which is actual in the voting theory. Other aspects of the population dynamics such as altruistic behavior or the battle of the sexes are closely connected to the mathematical sociobiology.

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