Oleg Makarenkov joined the UT Dallas faculty in 2013 as an Assistant Professor in the Department of Mathematical Sciences. His research interests are currently focused on "applications of the theory of dynamical systems to real-life models that involve sudden switches, discontinuities and jumps." This would include:
(Elsevier Ltd) Makarenkov, Oleg; Phung, Anthony; Makarenkov, Oleg; Phung, Anthony
For switched systems that switch between distinct globally stable equilibria, we offer closed-form formulas that lock oscillations in the required neighborhood of the equilibria. Motivated by non-spiking neuron models, the main focus of the paper is on the case of planar switched affine systems, where we use properties of nested cylinders coming from quadratic Lyapunov functions. In particular, for the first time ever, we use the dwell-time concept in order to give an explicit condition for non-spiking of linear neuron models with periodically switching current.