The parametric estimation of stochastic differential equations (SDEs) has been the subject of intense studies already for several decades. The Heston model, for instance, is based on two coupled SDEs and is often used in financial mathematics for the dynamics of asset prices and their...

A food web model with a closed nutrient cycle is presented and analyzed via Monte Carlo simulations. The model consists of three trophic levels, each of which is populated by animals of one distinct species. While the species at the intermediate level feeds on the basal species, and is eaten by...

A spatial three level food web model with a closed nutrient cycle is presented and analyzed via Monte Carlo simulations. The food web consists of three trophic levels. The basal level species (called resources, R) corresponds to primary producers in real ecosystems. The species at an...

We present and study a lattice (Monte Carlo) model of a food web consisting of three levels. Agents on the lowest level produce food from dead agents (detritus) of the upper levels and are themselves eaten by the first level species, which in turn are prey for the top level species. Agents which...

The influence of habitat destruction on a population of predators and prey is studied. We show, via Monte Carlo simulations of a lattice model, that with growing devastation the oscillations in the densities of both species, as well as cross-correlations between the two densities diminish. As...

Using the molecular-field approximation for the lattice gas model in terms of a spin-one Ising model, we construct phase diagrams and show when the transition could be of first or second order. Possible relevance to the theoritical models of phase transitions in monolayers of amphipatic...

A new model of one type of annual plant dynamics is proposed and discussed. The model is based on individual agents Monte Carlo simulations. We take into account, the plant requirements for external resources (sunshine, moisture etc.), competition among plants and the influence of accumulated...

Time evolution of a model of population of diploid organisms is studied using the Monte Carlo technique. Reproduction of the individuals follows the Mendelian rules, including the recombination. We compare the effects of harmful mutations and changes of the environment on the population size,...

Modeling the dynamics of interacting species (or populations) is a long standing problem in sciences which, in the recent years, has attracted a lot of physicists working in statistical physics. The similarities and differences between models of dynamics of population and usual statistical...

A model for economic behavior, under heterogeneous spatial economic conditions is developed. The role of selection pressure in a Bak–Sneppen-like dynamics with entity diffusion on a lattice is studied by Monte-Carlo simulation taking into account business rule(s), like enterprise–enterprise...