Positivity of solutions of (polynomial) differential equations

2020. 03. 12. 10:15
János Tóth

We present the deterministic model of chemical reactions and show why this is an important class of equations both from the point of view of the qualitative theory and of applications. 

Next, we review results on the positivity of the solutions of the model, starting from the continuously rediscovered results by Volpert (1972). The components of the solutions are either strictly positive or zero for all positive times of their domain. Which is which---this can be decided using the concept of Volpert indexes.

 As an application, we show one of the algorithms to find minimal sets of species that ensure the positivity of all the species concentrations during the domain of solutions.