UTA Department of Mathematics

Mathematics and Statistics Colloquium

Date/Time/Room: Friday (4/14/2006) at 2:30pm in 304 Pickard Hall

Speaker: Dr. Alexander V. Prasolov, Professor and Head
Department of Economical Systems Modeling
Faculty of Applied Mathematics - Control Processes, Saint-Petersburg State University


"Dynamic Competitive Analysis in the Automotive Industry"

Abstract: Many linear models in dynamics do not satisfactorily explain the process of dynamic competitive analysis in many fields such as biology, ecology, economics, and even n the automotive industry. Some alternative approaches to non-linear models are suggested, in particular the application of the well-known Lotka-Volterra models with delay. These types of models are appropriate because of their saturation effect and specific oscillation properties.

The dynamics for modeling the sale of small and medium size motor vehicles in the internal USA market for last several decades is considered in this investigation. American domestically produced cars compete against cars produced in foreign countries, principally in Europe, Japan, and Korea. A dynamic mathematical model is suggested in the form of two Lotka-Volterra type differential equations. The principle model properties are presented: equilibrium trajectories, asymptotic behavior, dissipation and variability. An emphasis is made in the approach to identify simultaneously the model parameters such as the coefficients and the time lag.