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Antipodeal Dynamics Workshop, 11th/12th December 2023

The fourth Auckland-Exeter virtual Antipodeal Dynamics Workshop will be held on Monday, December 11th 8-10pm (UK)/Tuesday, December 12th 9-11am (NZ). Three talks on Zoom will be followed be a virtual poster session hosted on Mozilla Hubs.

  • 8-8:20pm UK/9-9:20am NZ: Alexandre Rodrigues
  • 8:20-8:40pm UK/9:20-9:40am NZ: David Simpson
  • 8:40pm-9pm UK/9:40-10am NZ: Krasimira Tsaneva-Atanasova
  • 9-10pm UK/10-11am NZ: Virtual poster session

All welcome! Please register your interest using this form:

We welcome posters: these will be hosted in a virtual poster room using Mozilla Hubs. You can contact one of the organizers if you have any questions.


Alexandre Rodrigues (ISEG, University of Lisbon and CMUP, University of Porto): Stability of heteroclinic cycles using the projective map

In this talk we analyze the stability of cycles within a heteroclinic network formed by six cycles lying in a three-dimensional manifold, for a one-parameter model developed in the context of polymatrix replicator equations. We describe an asymptotic technique to decide which cycle (within the network) is visible in numerics. The technique consists of reducing the relevant dynamics to a suitable one-dimensional map, the so-called projective map. The stability of the fixed points of the projective map determines the stability of the associated cycles.

David Simpson (Massey University): Patterns of bifurcations in piecewise-smooth dynamical systems

Mathematical models in different areas of application exhibit many of the same bifurcation patterns. Classical examples include period-doubling cascades and structures associated with homoclinic and heteroclinic connections. Models incorporating switches, thresholds, or other abrupt events, however, are often piecewise-smooth and exhibit unique bifurcation patterns. In this talk I will review such structures centred around homoclinic corners which are a piecewise-smooth analogue of first homoclinic tangencies whereby a stable manifold collides with a kink of an unstable manifold.

Krasimira Tsaneva-Atanasova (University of Exeter): Saddle–node separatrix-loop bifurcation in neural mass models