Title: Bifurcation of limit cycles in nonsmooth differential equations with applications
Abstract: I will first present a result about bifurcation and discontinuous limit cycles in planar differential equations with impacts that we used to explain a phenomenon about spiking oscillations in a resonate-and-fire neuron model (with M. Hasselmo from Boston University). A dynamical phenomenon of potential applied interest here is that addition of an impacting surface allows to obtain limit cycles with significantly better stability property (if defined through the value of the characteristic multiplier of the associated 1-dimensional Poincare map). The second part of the talk will discuss a mechanism for bifurcation of limit cycles in discontinuous differential equations in #d that we used to explain the occurrence of glacial cycles in a conceptual climate model (with E. Widiasih from University of Hawai'i - West O'ahu). This bifurcation occurs when a switched equilibrium (a point on discontinuity hyperplane where the vector fields on the two sides of the hyperplane point towards one another) loses asymptotic stability.
Location & Time: CSL B02, November 5, 3-4PM
Reception in CSL 154 at 2:30PM
Bio: Since fall of 2019, I have been an Associate Professor with tenure in the Department of Mathematical Sciences at the University of Texas at Dallas. I joined UT Dallas on September 1, 2013 as a tenure-track Assistant Professor. Before this, I was a group leader at the Basque Center for Applied Mathematics (5-year contract started Sept 2012), a Humboldt Research Fellow at the University of Cologne (2-year contract started Jan 2012), a Marie Curie Fellow (2-year contract started Oct 2008) and Teaching Fellow (2-year contract) at Imperial College London, and a Junior Researcher at Voronezh State University (from June 2006).
I received my PhD in Mathematics from Voronezh State University in 2006 on the thesis "Topological Methods in Malkin-Melnikov problems on periodic perturbations of autonomous systems" under the supervision of Prof. M. Kamenskii. During my Master course (2004-2006) I took advantage of a 10-month research training in the University of Siena hosted by Prof. P. Nistri.
