My research interests focus around dynamical systems generated by retarded functional equations. What does “retarded” mean? Well, the question should be whether the future depends only on the present or also on the past.
Mathematically speaking, delay means an infinite-dimensional state space. Hence no surprise that, soon or later, one has to resort to numerical analysis. What for? Not just to compute a solution, but rather to investigate stability of equilibria and periodic orbits, or chaotic attractors.
In particular, I mainly work on numerical methods to approximate the spectra of those operators governing the linearized dynamics. Examples are solution operators, infinitesimal generators, monodromy operators and evolution families. Yes, there is a bit of functional analysis behind.
The application fields I deal with are relevant to models of epidemics or physiologically structured populations (consumer-resource dynamics, age-dependent populations) and problems of control arising in mechanical engineering (Mathieu equations) or similar (networks). Translated, I am talking about functional equations which can be with delay or advanced-retarded, of neutral type, simply differential or integro-differential, or even couplings of the latter.
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