Plenary Lecture

Deterministic and Stochastic Advertising Diffusion Models

Professor Mihaela Neamtu
Faculty of Economics and Business Administration
West University of Timisoara

Abstract: The paper presents two advertising diffusion models described by systems of nonlinear differential equations, where a firm devotes a fixed proportion of sales to advertising. In the first model the customers go through a two-stage adoption process, from non-adopter to adopter under the influence of word-of-mouth and advertising. There is time delay in the advertising response. In the second model the customers go through a three-stage adoption process: non-adopter-thinker-adopter. The thinker population is exposed to advertisement and will become adopter after some delay. For both models, the deterministic and stochastic versions are described. First, for the deterministic models, the equilibrium points are analyzed. Also, the stability of the Hopf bifurcation is provided. For the linearized perturbed stochastic system, the differential equations for the square mean values are identified and their dynamics are studied. The last part includes numerical simulations and conclusions.

Brief Biography of the Speaker:Mihaela Neamtu was born in Timisoara (Romania) on 1971. She graduated in 1995 the Faculty of Mathematics, West University of Timisoara. In 2001 she obtained the title of Ph.D in mathematics. She followed a didactic career at the Faculty of Economics and Business Administration, West University of Timisoara, Romania and she is currently a professor. She has been a visiting Professor for short periods of time at The Nottingham Trent University, Economics & Politics (Great Britain) and Faculty of Mathematics, Bonn (Germany). Professor Mihaela Neamtu has over 70 articles published in Journals and Proceedings of the International Conferences and 5 monographs; she has been a regular referee of papers for several International Journals and a reviewer of Mathematical Reviews (MathSciNet). She has been participating in 12 multiannual grants (1 of them is international), in 9 as a member and in 2 as a director. Her main academic interests are in dynamical systems and applications in biology and economy.