Population models represent an important field in Biomathematics. They give information and forecast about dynamics of the population. This talk will give an insight about population dynamics models in general and we will talk about two such models in detail. We will start with the stability analysis of the Easter Island population dynamics model than we will take a look at the numerical methods for the Lotka-Volterra system.
When investigating the deterministic and/or stochastic models of chemical reactions a large amount of calculations have to be carried out. The preliminary steps are creating and studying different graphs describing reactions. This involves the use of combinatorics and linear algebra. One is also interested if mass is conserved in a model or not. This can be decided using the methods of linear programming. Stationary points and stationary distributions are to be determined which means the solution of large polynomial equations. One has to solve (quite often: stiff) ordinary differential equations, simulate Markovian jump processes. Parameters of these processes are to be estimated based on measurements even in cases when not all the concentration time curves are known. This problem is implicit and highly nonlinear. Our package gives help to all these tasks arising in chemistry (atmospheric chemistry), biochemistry (modeling metabolism), chemical engineering (combustion), but the models of chemical reaction kinetics are used outside chemistry, as well. We show the problems and solution methods from the point of programming and also a series of applications. A comparison with other programs will also be presented. A detailed description and instructions for use will be found in our book: J. Tóth, A. L. Nagy, D. Papp: Reaction Kinetics: Exercises, Programs and Theorems. (Mathematica for deterministic and stochastic kinetics), Springer, 2018 (to appear). (Joint talk with A. L. Nagy and D. Papp.)