A population dynamical model of Operophtera brumata, L. extended by climatic factors

Setting out from the database of Operophtera brumata, L. in between 1973 and 2000 due to the Light Trap Network in Hungary, we introduce a simple theta-logistic population dynamical model based on endogenous and exogenous factors, only. We create an indicator set from which we can choose some elements with which we can improve the fitting results the most effectively. Than we extend the basic simple model with additive climatic factors. The parameter optimization is based on the minimized root mean square error. The best model is chosen according to the Akaike Information Criterion. Finally we run the calibrated extended model with daily outputs of the regional climate model RegCM3.1, regarding 1961-1990 as reference period and 2021-2050 with 2071-2100 as future predictions. The results of the three time intervals are fitted with Beta distributions and compared statistically. The expected changes are discussed.

An agro-ecological simulation model system

In this paper five different models, as five modules of a complex agro-ecosystem are investigated. The water and nutrient flow in soil is simulated by the nutrient-in-soil model while the biomass change according to the seasonal weather aspects, the nutrient content of soil and the biotic interactions amongst the other terms of the food web are simulated by the food web population dynamical model that is constructed for a piece of homogeneous field. The food web model is based on the nutrient-in-soil model and on the activity function evaluator model that expresses the effect of temperature. The numbers of individuals in all phenological phases of the different populations are given by the phenology model. The food web model is extended to an inhomogeneous piece of field by the spatial extension model. Finally, as an additional module, an application of the above models for multivariate state-planes, is given. The modules built into the system are closely connected to each other as they utilize each other’s outputs, nevertheless, they work separately, too. Some case studies are analysed and a summarized outlook is given.

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.