# Dynamical systems

Wednesday, March 16, 2016 - 4:30pm - 5:00pm

Eldad Haber (University of British Columbia)

While optimal experimental design for static linear inverse problems has been well studied, there is little in the way of experimental design methods for dynamical systems. In particular, dynamic problems where historic data is included in the optimal experimental design method, such that the experiment tracks the motion of the model.

Monday, November 16, 2015 - 11:30am - 12:30pm

Matthew Bennett (Rice University)

Synthetic biology aims to engineer biological systems for practical purposes through the manipulation of gene regulation and enzymatic processes within the host. The vast majority of synthetic gene circuits operate within a single cell or isogenic colony of bacteria. However, utilizing multiple strains or species of bacteria simultaneously could greatly expand the possibilities of synthetic biology. These systems, called synthetic microbial consortia, more closely resemble the naturally heterogeneous environments of bacteria, such as gut microbiomes or biofilms.

Friday, August 14, 2015 - 10:00am - 10:30am

Vera Nuebel (Hilti Corporation)

Monday, November 1, 2010 - 12:00pm - 12:45pm

Claudio Canuto (Politecnico di Torino)

We are witnessing an increasing interest for cooperative

dynamical systems proposed in the recent literature as possible

models for

opinion dynamics in social and economic networks.

Mathematically,

they consist of a large number, N, of 'agents' evolving

according to

quite simple dynamical systems coupled in according to some

'locality'

constraint. Each agent i maintains a time function

x

representing the 'opinion,' the 'belief' it has on something.

dynamical systems proposed in the recent literature as possible

models for

opinion dynamics in social and economic networks.

Mathematically,

they consist of a large number, N, of 'agents' evolving

according to

quite simple dynamical systems coupled in according to some

'locality'

constraint. Each agent i maintains a time function

x

_{i}(t)representing the 'opinion,' the 'belief' it has on something.

Tuesday, March 6, 2007 - 1:30pm - 2:20pm

Martin Golubitsky (University of Houston)

A coupled cell system is a collection of interacting dynamical systems.

Coupled cell models assume that the output from each cell is important and

that signals from two or more cells can be compared so that patterns of

synchrony can emerge. We ask: How much of the qualitative dynamics observed

in coupled cells is the product of network architecture and how much depends

on the specific equations? Speficially we study the structure of

synchrony-breaking bifurcations in these systems.

Coupled cell models assume that the output from each cell is important and

that signals from two or more cells can be compared so that patterns of

synchrony can emerge. We ask: How much of the qualitative dynamics observed

in coupled cells is the product of network architecture and how much depends

on the specific equations? Speficially we study the structure of

synchrony-breaking bifurcations in these systems.

Monday, April 20, 2015 - 10:00am - 11:00am

Tuhin Sahai (United Technologies Corporation), Sumanth Swaminathan (W. L. Gore & Associates)

**Tuhin Sahai**: Dynamical Systems and Continous Approximations for NP-hard Problems

Monday, February 10, 2014 - 10:15am - 11:05am

Bob Rink (Vrije Universiteit)

Dynamical systems with a coupled cell network structure arise in applications that range from statistical mechanics and electrical circuits to neural networks, systems biology, power grids and the world wide web.

Wednesday, May 15, 2013 - 2:00pm - 2:50pm

Lee DeVille (University of Illinois at Urbana-Champaign)

We will consider stochastic dynamical systems defined on networks that exhibit the phenomenon of collective metastability---by this we mean network dynamics where none of the individual nodes' dynamics are metastable, but the configuration is metastable in its collective behavior. In particular, we show how many biological oscillators --- both pulse-coupled and phase-coupled --- fall into this framework. We also examine a non-standard spectral problem that generically appears in these problems.

Thursday, September 6, 2012 - 3:30pm - 4:30pm

Chai Wah Wu (IBM)

We look at complex networks of coupled dynamical systems where an external forcing control signal is applied to the network in order to align the state of all the individual systems to the forcing signal. We study how the effectiveness of such control is related to the topology of the underlying graph. For instance, we show that for the cycle graph, the best way to achieve control is by applying control to systems that are approximately equally spaced apart.

Thursday, October 25, 2012 - 10:15am - 11:05am

Zeng Lian (Loughborough University)

Lyapunov exponents play an important role in the study of the behavior of dynamical systems. They measure the average rate of separation of orbits starting from nearby initial points. They are used to describe the local stability of orbits and chaotic behavior of systems. Multiplicative Ergodic Theorem provides the theoretical foundation of Lyapunov exponents, which gives the fundamental information of Lyapunov Exponents and their associates invariant subspaces.