Dynamics of bipolar disorders model: periodic and switching phenomenon, joint work with E. Kutafina and P. Szmolyan, in preparation.
Papers in journals
2015 I.K, P. Szmolyan, Geometric analysis of Goldbeter’s model for the mitotic oscillator, J. Math. Biol. DOI 10.1007/s00285-015-0905-0
2011 I.K, P. Szmolyan, Scaling in Singular Perturbation Problems Blowing Up a Relaxation Oscillator, SIAM J. Appl. Dyn. Syst.,10, pp. 1307-1343
2010 I.K, P. Szmolyan, Geometric Desingularization in Slow-Fast Systems with Application to the Glycolytic Oscillations Model, AIP Conf. Proc., 1281 (2010) pp. 235-238
2009 I. Gucwa, P. Szmolyan, Geometric singular perturbation analysis of an autocatalator model, Discrete and Continuous Dynamical Systems Series S, 2 (2009) pp. 783-806
2007 I. Gucwa, N. N. Bogoliubov (Jr.), A. K. Prykarpatski, and J. Golenia, Analytical properties of an Ostrovsky-Whitham type dynamical system for a relaxing medium with spatial memory and its integrable regularization, Preprint IC/2007/109, The Abdus Salam International Center for Theoretical Physics, Trieste, Italy
2012 Relaxation oscillations in slow-fast systems beyond the standard form, Dissertation, University of Leipzig, supervised by Prof. J. Jost