Differential equations are the mathematical descriptions of physical and biological systems that continuously change in time. These equations are defined by relationships between the current state of the system and the rate of its change. Our goal is to predict the future behaviour of the system, using analytic, qualitative or numerical investigations of the solutions.
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.
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.
Cell proliferation, death and motility are key events in many important cell biological processes, such as embryonic development, tissue regeneration or the progression of cancer. Mathematical models help to understand the collective behaviour and the spatio-temporal dynamics of various cell populations, which may lead to, for example, more efficient treatments of cancer.
Bifurcations represent situations when the behaviour of a system suddenly changes as a parameter is crossing a critical value. They are associated to loss of stability, the appearance or destruction of equilibria, sudden emergence of periodic or more complex behaviours. The birth of chaos from simple dynamics can be understood through a cascade of subsequent bifurcations.
|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)|