Non-uniqueness through duality in the von Neumann growth models

Duality can be viewed as the soul of each von Neumann growth model. This is not at all surprising because von Neumann (1955), a mathematical genius, extensively studied quantum mechanics which involves a “dual nature” (electromagnetic waves and discrete corpuscules or light quanta). This may have had some influence on developing his own economic duality concept. The main object of this paper is to restore the spirit of economic duality in the investigations of the multiple von Neumann equilibria. By means of the (ir)reducibility taxonomy in Móczár (1995) the author transforms the primal canonical decomposition given by Bromek (1974) in the von Neumann growth model into the synergistic primal and dual canonical decomposition. This enables us to obtain all the information about the steadily maintainable states of growth sustained by the compatible price-constellations at each distinct expansion factor.

Nemlineáris dinamika klasszikus növekedési modellekben (Nonlinear dynamics in classical economic growth models)

Ebben a tanulmányban a klasszikus Harrod növekedési modellt nemlineáris kiterjesztéssel, keynesi és schumpeteri tradíciók bevezetésével reprezentatív ügynök modellbe alakítjuk. A híres Lucas kritika igazolásaként megmutatjuk, hogy az intrinsic gazdasági növekedési ütemek trajektóriái vagy egy turbulens káoszba szóródnak szét, vagy egy nagyméretű rendhez vezetnek, ami elsődlegesen a megfelelő fogyasztási függvény típusától függ, s bizonyos paraméterek piaci értékei, pedig csak másodlagos szerepet játszanak. A másik meglepő eredmény empirikus, ami szerint külkereskedelmi többlet, a hazai valuta bizonyos devizapiaci értékei mellett, különös attraktorokat generálhat. _____ In this paper the classical Harrodian growth model is transformed into a representative agent model by its nonlinear extensions and the Keynesian and Schumpeterian traditions. For the proof of the celebrated Lucas critique it is shown that the trajectories of intrinsic economic growth rates either are scattered into a turbulent chaos or lead to a large scale order. It depends on the type of the appropriate consumption function, and the market values of some parameters are playing only secondary role.Another surprising result is empirical: the international trade su±cit may generate strange attractors under some exchange rate values.

A Harrod modell strukturális stabilitása (Structural stability of the Harrod model)

In this study it is shown that the nontrivial hyperbolic fixed point of a nonlinear dynamical system, which is formulated by means of the adaptive expectations, corresponds to the unstable equilibrium of Harrod. We prove that this nonlinear dynamical (in the sense of Harrod) model is structurally stable under suitable economic conditions. In the case of structural stability, small changes of the functions (C1-perturbations of the vector field) describing the expected and the true time variation of the capital coefficients do not influence the qualitative properties of the endogenous variables, that is, although the trajectories may slightly change, their structure is the same as that of the unperturbed one, and therefore these models are suitable for long-time predictions. In this situation the critique of Lucas or Engel is not valid. There is no topological conjugacy between the perturbed and unperturbed models; the change of the growth rate between two levels may require different times for the perturbed and unperturbed models.

Simulations of Theoretical Ecosystem Growth Model (TEGM) during various climate conditions

Climate change has a great impact on the build and the work of natural ecosystems. Disappearance of some population or growth of the number in some species can be already caused by little change in temperature. A Theoretical Ecosystem Growth Model was investigated in order to examine the effects of various climate patterns on the ecological equilibrium. The answers of the ecosystems which are given to the climate change could be described by means of global climate modelling and dynamic vegetation models. The examination of the operation of the ecosystems is only possible in huge centres on supercomputers because of the number and the complexity of the calculation. The number of the calculation could be decreased to the level of a PC by considering the temperature and the reproduction during the modelling of a theoretical ecosystem and several important theoretical questions could be answered.

Simulation modeling of phytoplankton dynamics in a large eutrophic river, Hungary – Danubian Phytoplankton Growth Model (DPGM)

Ecological models have often been used in order to answer questions that are in the limelight of recent researches such as the possible effects of climate change. The methodology of tactical models is a very useful tool comparison to those complex models requiring relatively large set of input parameters. In this study, a theoretical strategic model (TEGM ) was adapted to the field data on the basis of a 24-year long monitoring database of phytoplankton in the Danube River at the station of G¨od, Hungary (at 1669 river kilometer – hereafter referred to as “rkm”). The Danubian Phytoplankton Growth Model (DPGM) is able to describe the seasonal dynamics of phytoplankton biomass (mg L−1) based on daily temperature, but takes the availability of light into consideration as well. In order to improve fitting, the 24-year long database was split in two parts in accordance with environmental sustainability. The period of 1979–1990 has a higher level of nutrient excess compared with that of the 1991–2002. The authors assume that, in the above-mentioned periods, phytoplankton responded to temperature in two different ways, thus two submodels were developed, DPGM-sA and DPGMsB. Observed and simulated data correlated quite well. Findings suggest that linear temperature rise brings drastic change to phytoplankton only in case of high nutrient load and it is mostly realized through the increase of yearly total biomass.