New Zealand Mathematics Research Institute (Inc.) 2016 NZMRI Summer School The University of Auckland

Continuation Methods in Dynamical Systems

Raglan, 10-15 January 2016
followed by Hands-On Workshop at The University of Auckland, 18-19 January 2016

Organisers:Bernd Krauskopf
Hinke Osinga

NZMRI 2016 group photo

The January 2016 NZMRI Summer meeting Continuation Methods in Dynamical Systems will be held in Raglan from 10-15 January 2016. The meeting will start in the afternoon of Sunday 10th with an overview and introductory lectures aimed at participating postgraduates. The invited speakers will give lectures in the mornings and the afternoons will be free for informal discussions. Furthermore, we will introduce student-led evening sessions to increase interactions between lecturers and students and help with understanding the material covered each day. Following the NZMRI Summer school, there will be a separate course to gain hands-on experience with numerical continuation software, held at The University of Auckland on 18 and 19 January.

The programme is available for more information.

Bus transportation for delegates: The bus will depart from Auckland at 10am on Sunday, 10 January 2016
Departure is from the bus stop outside the main library on Alfred Street (city campus)
Delegates are expected to arrive by 9:50am
Summer School venue: Raglan Sunset Motel
7 Bankart St, Raglan 3225

Invited speakers

Harry Dankowicz John Guckenheimer Tony Humphries Jan Sieber Krasimira Tsaneva-Atanasova
University of Illinois, Urbana-Champaign, USA Cornell University, Ithaca NY, USA McGill University, Montreal, Canada University of Exeter, Exeter, UK University of Exeter, Exeter, UK

Harry Dankowicz, University of Illinois, Urbana-Champaign, USA
 Harry Dankowicz conducts dynamical systems research at the intersection of engineering, mathematics and physics. His work involves studying a wide range of complex systems that are governed by differential equations, learning the behaviour of those systems through theory and experiments, and contributing to the development and design of existing or novel devices or methodologies that capitalise on system nonlinearities for improved system understanding and performance. Harry’s lectures at the Summer School will explain and demonstrate parameter continuation and multi-dimensional manifold analysis using the software package COCO (which he developed with Frank Schilder), with particular emphasis on multi-segment boundary-value problems. He will also be contributing to the Hands-On Workshop with COCO tutorial demos and support.
John Guckenheimer, Cornell University, Ithaca NY, USA
 John Guckenheimer has made many contributions to dynamical systems an bifurcation theory. Much of his work the past fifteen years has been devoted to geometric and computational analysis of systems with multiple time scales, the subject of his lectures at this Summer School. Different types of invariant manifolds will be introduced, and their role in global bifurcations will be discussed. Mechanisms by which multiple time scales give rise to complex oscillations (bursting and mixed-mode oscillations) will be described. The lectures will illustrate ideas with examples rather than concentrate on proving theorems.
Tony Humphries, McGill University, Montreal, Canada
 Tony Humphries is an expert in the numerical analysis of dynamical systems. His research interests include state-dependent delay differential equations and applications in mathematical physiology. At the Summer School he will talk about numerical methods for delay differential equations, concentrating on numerical bifurcation analysis and the continuation of periodic orbits.
Jan Sieber, University of Exeter, Exeter, UK
 Jan Sieber's general research area is applied dynamical systems. His interests lie in the development of numerical continuation methods for physical experiments, differential equations with delay, and models where many interacting components combine to show emerging macroscopic bifurcations. During the Summer School, Jan will discuss continuation methods in different contexts and, in particular, will show how one can perform bifurcation analysis in experiments. As the maintainer of the Matlab/octave compatible bifurcation analysis tool DDE-Biftool, he will contribute to the Hands-On Workshop with DDE-Biftool specific problems and provide a few examples of systems with emerging bifurcations (for example, an adaptive network on which an SIS-type disease spreads, as studied by Gross et al).
Krasimira Tsaneva-Atanasova, University of Exeter, Exeter, UK
 Krasimira Tsaneva-Atanasova is a recognised expert in applications of dynamical systems theory to problems in mathematical neuroscience and (neuro)endocrinology and she is currently involved in large collaborative research projects investigating novel applications of mathematics to enable the development of quantitative methods for healthcare and healthcare technologies. In her work she investigates how complicated transitions to different dynamic regimes manifest themselves in the full phase space of a given dynamical system, and hence, explain physiologically relevant function of the real-world system it represents. At the Summer School Krasimira will discuss how bifurcation analysis/continuation can be employed in biological systems, including in electrophysiology experiments and in human-computer interaction.


The venue for the Summer School is the small seaside town of Raglan, located on the west coast of the North Island of New Zealand, approximately 160km South of Auckland.

(Optional) Bus transportation from Auckland to Raglan will be available to delegates
Summer School in Raglan: Arrive in time for lunch on Sunday, 10 January 2016
Depart after lunch on Friday, 15 January 2016

(Optional) Bus transportation from Raglan to Auckland will be available to delegates

The Hands-On Workshop will be held at the University of Auckland and is intended for participants who wish to implement their own models and receive help from the experts.

Hands-On Workshop in Auckland: Starts 9:30am on Monday 18 January 2016
Ends 5pm on Tuesday 19 January 2016

The programme is available for more information.

These events are generously supported by the NZMRI, with additional support from The University of Auckland; see the information about costs. Students at New Zealand universities are invited to apply for a Kalman Summer Scholarship to help cover costs of their participation.


Places are limited and registration by 30 October 2015 is strongly encouraged. To register for the NZMRI Summer School, the Hands-On Workshop, or both, please, follow the instructions on the registration page.

If you have any questions, please, email the organisers on

Copyright © 2015 by Hinke Osinga
Last modified: Tue Dec 22 16:53:46 NZDT 2015