Time delays arise in various fields of engineering, physics and biology. Dynamical systems including delays can be written as delay differential equations (DDEs). Their right hand side is a functional, and the corresponding phase space is infinite dimensional. Nonlinear DDEs can show very interesting dynamics and lead to fascinating and sophisticated mathematics.
Nonlinear dynamics describe the time evolution of systems where the output is not proportional to the input. To understand complex systems we need to take into account all the interactions of variables and complicated feedbacks. A major goal is to describe the geometric structure of attractors, that encapsulate the most important information about the long term dynamics.
Mathematical models can predict how infectious diseases progress to show the likely outcome of an epidemic. By disease modelling we can provide important information to public health by designing, evaluating and comparing different strategies to control the outbreak. The basic mathematical framework uses systems of differential equations called compartmental models.
|2017 - 2018||TEMPOMATH||EU Marie Sklodowska-Curie Individual Fellowship No. 748193|
|2011 - 2016||EPIDELAY||European Research Council Starting Investigator Grant No. 259559|
|2017 - 2019||Dynamics and Control of Metapopulations||National Research, Development and Innovation Office NKFI KH 125628|
|2017 - 2021||Functional Differential Equations in Mathematical Epidemiology||National Research, Development and Innovation Office NKFI FK 124016|
|2018 - 2019||Applications of Dynamical Systems in Population Biology||TET16JP Hungary-Japan Bilateral Project (with H. Inaba, JSPS)|