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Antipod(e)al heteroclinic workshop, 5th October 2020

There will be a collaborative workshop by Zoom on dynamical systems (with focus on heteroclinic dynamics) on 5th October 2020, 8-10am (UK), 8-10pm (NZ).

  • 8:00 Introduction and welcome
  • 8:05-8:20 Valerie Jeong (Auckland) “A noisy, perturbed heteroclinic cycle and evolutionary robotics”
  • 8:25-8:40 Chris Bick (Exeter) “Heteroclinic dynamics in phase oscillator networks with higher order interactions”
  • 8:45-9:00 Gray Manicom (Auckland) “A network model of task-switching”
  • 9:05-10:00 Virtual reality poster session (Jen Creaser, Max Voit, Gray Manicom, Valerie Jeong)

All welcome! Please write to one of the organizers to be emailed the links and/or if you have a poster you wish to display.

Peter Ashwin (Exeter)

Claire Postlethwaite (Auckland)



Valerie Jeong “A noisy, perturbed heteroclinic cycle and evolutionary robotics”

Abstract: Evolutionary robotics is a methodology for a machine learning type problem. An artificial neural network (the controller of a robot) is evolved so that the robot can complete a given task. In a given environment, a robot receives sensory inputs from objects that are related to the task, and these play a key role when evolving the controller. Previous work has shown that small noise can play a significant role in improving a robot’s performance.

One way to model the controller is to use a continuous dynamical structure called a heteroclinic network. The sensory inputs that a robot receives correspond to perturbations to a heteroclinic network. To analyse the resulting behaviour of a robot after evolution, we need a better understanding of the effects of perturbations and/or noise on a heteroclinic network. A heteroclinic network can exhibit interesting dynamics when small noise and/or perturbations are added. In particular, we expect the residence time near equilibria of a heteroclinic network to monotonically decrease as noise gets larger. However, we observe an increase in the residence time for a certain range of noise when both perturbations and noise are added.

In this talk, I will discuss a heteroclinic cycle called the Guckenheimer-Holmes cycle, and how the addition of small noise and/or perturbations change the dynamics. I will also illustrate a general setting for an Evolutionary Robotics task with examples.

Gray Manicom “A network model of task-switching”

Abstract: Psychologists have long been interested in the delay that occurs when people switch from performing one task to performing another task, called a switch cost. In this talk I will propose a model of task-switching that uses a mixed heteroclinic and excitable network.

The time it takes to complete a task is modeled by the time it takes to complete one of the cycles within the network. Input is added to the network so that there are transitions along the excitable connections and so that an appropriate sequence of cycles is followed. This construction allows the network to have memory such that the time it takes to complete a cycle is dependent on which cycle was most recently traversed. Thus, the model to reproduce the characteristic patterns associated with the switch cost observed in experiments.



Jen Creaser (Exeter)

Valerie Jeong (Auckland) “Evolving robots that have heteroclinic brains”

Gray Manicom (Auckland) “Noisy heteroclinic networks”

Max Voit (Bremen) “Learning (in) heteroclinic networks”

Workshop: Network Approaches for Healthcare Applications, 30-31 March 2020


This workshop in Exeter will involve the Centre for Systems, Dynamics and Control as well as the Centre for Predictive Modelling in Healthcare:  for more details and to register, see:


Position available: Postdoctoral Research Fellow in Dynamical Systems

Applications are invited for a Postdoctoral Research Fellow in Dynamical Systems (Job Ref P71641) at the University of Exeter, closing date 4th February 2020.

You will join the EPSRC funded project “Applied Nonautonomous Dynamical Systems: Theory, Methods and Examples” led by Prof Peter Ashwin to undertake fundamental research into theoretical aspects of nonautonomous dynamical systems, and applications to the climate system. You will be based at Exeter but will work collaboratively with the EPSRC-funded team that includes co-investigators Martin Rasmussen (Imperial College London) and Valerio Lucarini (University of Reading) as well as project partners Prof Sebastian Wieczorek (Cork), the EU-TiPES project (EU, led from Copenhagen) and Richard Wood (Met Office Hadley Centre). The task will be to work within a team that contributes to the development of applicable numerical and theoretical tools for nonautonomous systems, suitable for application to climate models.

Further information is available here

New postdoctoral researcher

We welcome Julian Newman who has just joined the Centre for Systems, Dynamics and Control (and the Maths department) as a postdoctoral fellow on the EU funded TiPES (Tipping points in the Earth system) project: https://tipes.sites.ku.dk/.

He will be working with Peter Ashwin and Jan Sieber on aspects of the mathematical theory of tipping points for nonautonomous systems. Julian did his PhD at Imperial College in 2016 and recently was working as a postdoc at the University of Lancaster.

Postdoctoral research fellow: Mathematics of Tipping Points in Complex Dynamical Systems

Mathematics of Tipping Points in Complex Dynamical Systems

This post is available for 36 months from 2  September 2019.

Details and to apply: https://www.jobs.ac.uk/job/BSM616/postdoctoral-research-fellow

Summary of the role/position
You will join the EU-funded H2020 project “Tipping Points of the Earth System” (TiPES) and undertake research into theoretical and applied aspects of tipping points and of relevance to complex multiscale systems such as the Earth system.

Several subsystems of the Earth may respond abruptly at critical future levels of anthropogenic forcing, which have been associated with tipping points (TPs). TiPES aims to identify safe operating spaces in terms of critical forcing levels. The TiPES project is a joint project involving 18 European institutions, combining paleoclimatology, time series analysis, Earth system modelling of past and future climates, applied mathematics and dynamical system theory, as well as decision theory.

You will participate in the development of mathematical theory to underpin safe operating space for the earth system in the presence of tipping points. You will primarily contribute to work package WP5 of the TiPES project, which addresses “The theoretical underpinning for safe operating spaces in the presence of TPs”. You will be expected to develop tools that are applicable to classify, predict, quantify and mitigate TPs, in collaboration with other work packages.

The post will be based within the Department of Mathematics and Research Centres related to theoretical and applied dynamical systems, climate modelling and strong links to interdisciplinary Research Institutes.

Conference in Dynamics, Number Theory and Geometry

There will be a half-day conference in dynamics, number theory, and geometry.

Venue:  University of Exeter

Date:  05 April 2019 (Friday) Afternoon.

The workshop is organized by Dr Jimmy Tseng (Exeter) and more details are on:


The dynamics of a piecewise isometry

Pedro Peres, a PhD student within the Centre, has recently produced a short YouTube video that illustrates some aspects of the dynamics of a piecewise isometry that he has been studying as part of his reseach. You can find more about his work on the mathematics of this system in https://arxiv.org/abs/1805.00245.



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