Dynamical Systems Seminars
The Dynamical Systems seminar is held on Monday afternoon at
4:00 PM in MCS 148. Tea beforehand at 3:45 PM in MCS 153.
- September 15: No seminar; come to the BU/Keio Dynamics Workshop instead!
- September 22: Kelly
Title: Oscillons near Hopf bifurcations of planar forced reaction diffusion
Abstract: Oscillons are planar, spatially localized, temporally oscillating,
radially symmetric structures. They have been observed in various experimental
contexts, including fluid systems, granular systems, and chemical
systems. Oscillons often arise near forced Hopf birurcations.
It is known that small amplitude localized solutions to the planar forced
complex Ginzburg-Landau equation (fCGL) exist near onset. Using spatial
dynamics, we show that the dynamics on the center manifold of a periodically
forced reaction difuusion equation (fRD) near a Hopf bifurcation can be
captured by the fCGL. Thus, oscillon solutions to the fRD can be thought of as
a foliation over localized solutions to the fCGL. The is a work in progress,
joint with Bjorn Sandstede.
- September 29: Theo Vo (BU)
Title: Geometric Singular Perturbation Analysis of Mixed-Mode Dynamics in
Abstract: Pseudo-plateau bursting is a type of oscillatory waveform associated
with mixed mode dynamics in slow/fast systems and commonly found in neural
bursting models. Multiple methods from dynamical systems theory have been used
to understand these bursting rhythms, which are typically treated as
2-timescale problems. In the first part of this work, we demonstrate that the
two most common analysis techniques are different unfoldings of a 3-timescale
system. Our analysis shows that canards are a key feature of these systems
that locally organise the dynamics in phase space.
Canards are closely associated with folded singularities and in the case of
folded nodes, lead to a local twisting of invariant manifolds. Folded node
canards and folded saddle canards (and their bifurcations) have been studied
extensively. The folded saddle-node (FSN) is the codimension-1 bifurcation
that gives rise to folded nodes and folded saddles. Their dynamics however,
are not well-understood. In the second part of this work, we extend canard
theory into the FSN regime by combining methods from geometric singular
perturbation theory (blow-up), and the theory of dynamic bifurcations
(analytic continuation into the plane of complex time).
- October 6: Evelyn Sander (George Mason University)
Title: The Dynamics of Nucleation
Abstract: The Cahn-Hilliard equation is one of the fundamental models to describe
phase separation dynamics in metal alloys. In this talk, I will focus on
applying traditional dynamical tools, such as bifurcation theory and
computational topology in order to gain a better understanding of the
droplet formation during nucleation for the stochastic Cahn-Hilliard
equation. I will consider different types of noise and different types
of boundary conditions.
- October 13: Columbus Day; no seminar.
- October 20: Hans Kaper
(Georgetown and UIUC)
- October 27: Semyon Dyatlov (MIT)
- November 3: Raj Prasad
Title: "Infinite Measure Preserving Transformations and Tilings of the Integers
Associated to them."
- November 10:
- November 17: Doug Wright (Drexel)
- November 24:
- December 1: Osman
- December 8:
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