2018-2.1.11-TÉT-SI-2018-00007 – Qualitative and Computational Methods for Biochemical and Engineering Models

Beneficiary name: Obuda University
Project ID: 2018-2.1.11-TÉT-SI-2018-00007
Contracted funding amount: HUF 1,986,800
Funding rate: 100%
Project duration: 01/06/2019 – 31/05/2022

Project description:
In order to understand and influence the behavior of technical and biological systems, we need to be able to create and analyze the model of these systems. Some properties can be checked symbolically, however, some properties need to be examined using computational techniques. The results of our research will contribute to design processes, technological advancement and security improvement. The aim of our research is further development of qualitative and computational methods of analysis and control of differential equations with polynomial or rational right-hand side, such differential equations typically model the dynamics of biological and many technical models. In our common research we will develop methods to detect Hopf and Bautin bifurcations in ordinary differential equations with polynomial or rational right-hand side and many  parameters, and we will develop computational methods to find limit cycles. We will also further develop the waveform iteration technique to improve the numerical solutions of the differential equations. We will develop analysis methods for deciding if dynamic systems with differential equation having polynomial right-hand side are controllable using strictly positive input; we determine the minimal number of species of a chemical reaction (and the species themselves) whose inflow should be control inputs such that the reaction is controllable, moreover, we determine the minimal number of species of a chemical reaction (and the specific species) that need to be present initially to ensure the positivity of the other species in the reaction (later) in the process (i.e. the reaction will be realized).