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Antipodal 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”

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