Abstract: In this paper the static model of the Cournot duopoly with tax evasion, the dynamic model of the Cournot duopoly with tax evasion and the rent seeking game with tax evasion and time delay are presented. A study for the local stability of the stationary states is carried out. Also, the stochastic approach is taken into consideration. A Wiener process is used to describe the stochastic model, as the noise has a stabilization effect. The dynamics are studied in terms of stochastic stability in the stationary state, by constructing the Lyapunov exponent, depending on the parameters that describe the model. Also, the Lyapunov function is determined in order to analyze the mean square stability. The numerical simulations justify the theoretical results. Moreover, the hybrid models are associated to the deterministic models using the Wiener and Liu processes. Numerical simulations are performed for the above mentioned processes. Finally, conclusions regarding the economic processes are provided.

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 50 articles published in Journals and Proceedings of the International Conferences and 3 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 10 multiannual grants (1 of them is international), in 8 as a member and in 2 as a director. Her main academic interests are in dynamical systems and applications in biology and economy, geometrical mechanics.