Non-linear models: applications in economics

The study concentrated on demonstrating how non-linear modelling can be useful to investigate the behavioural of dynamic economic systems. Using some adequate non-linear models could be a good way to find more refined solutions to actually unsolved problems or ambiguities in economics. Beginning with a short presentation of the simplest non-linear models, then we are demonstrating how the dynamics of complex systems, as the economic system is, could be explained on the base of some more advanced non-linear models and using specific techniques of simulation. We are considering the non-linear models only as an alternative to the stochastic linear models in economics. The conventional explanations of the behaviour of economic system contradict many times the empirical evidence. We are trying to demonstrate that small modifications in the standard linear form of some economic models make more complex and consequently more realistic the behaviour of system simulated on the base of the new non-linear models. Finally, few applications of non-linear models to the study of inflation-unemployment relationship, potentially useful for further empirical studies, are presented.non-linear model; continuous time map; strange attractor; fractal dimension; natural unemployment

Non-linear models: applications in economics

The study concentrated on demonstrating how non-linear modelling can be useful to investigate the behavioural of dynamic economic systems. Using some adequate non-linear models could be a good way to find more refined solutions to actually unsolved problems or ambiguities in economics. Beginning with a short presentation of the simplest non-linear models, then we are demonstrating how the dynamics of complex systems, as the economic system is, could be explained on the base of some more advanced non-linear models and using specific techniques of simulation. We are considering the non-linear models only as an alternative to the stochastic linear models in economics. The conventional explanations of the behaviour of economic system contradict many times the empirical evidence. We are trying to demonstrate that small modifications in the standard linear form of some economic models make more complex and consequently more realistic the behaviour of system simulated on the base of the new non-linear models. Finally, few applications of non-linear models to the study of inflation-unemployment relationship, potentially useful for further empirical studies, are presented

Period doubling and reducibility in the quasi-periodically forced logistic map

We study the dynamics of the Forced Logistic Map in the cylinder. We compute a bifurcation diagram in terms of the dynamics of the attracting set. Different properties of the attracting set are considered, as the Lyapunov exponent and, in the case of having a periodic invariant curve, its period and its reducibility. This reveals that the parameter values for which the invariant curve doubles its period are contained in regions of the parameter space where the invariant curve is reducible. Then we present two additional studies to explain this fact. In first place we consider the images and the preimages of the critical set (the set where the derivative of the map w.r.t the non-periodic coordinate is equal to zero). Studying these sets we construct constrains in the parameter space for the reducibility of the invariant curve. In second place we consider the reducibility loss of the invariant curve as codimension one bifurcation and we study its interaction with the period doubling bifurcation. This reveals that, if the reducibility loss and the period doubling bifurcation curves meet, they do it in a tangent way

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008