There will be a further collaborative Virtual Workshop on Dynamical Systems on Wednesday 12th October 2020, 8-10pm (UK), Thursday 13th October, 8-10am (NZ).
- 8:00-8:20 Yuri Bakhtin (NYU) “Rare transitions in noisy heteroclinic networks”
- 8:20-8:40 George Datseris (Hamburg/Exeter) “Methods and software for estimating basins of attraction of arbitrary dynamical systems”
- 8:40-9:00 Lauren Smith (Auckland) “Swarmalators with second order phase coupling: Syncing, swarming and clustering”
- 9:00-10:00 Virtual reality poster session
All welcome! Please register your interest using this form:
https://forms.gle/SSgqUmckZA7xZ17n6
We welcome posters: these will be hosted in a virtual reality poster room using Mozilla Hubs. You can contact one of the organizers if you have any questions.
Peter Ashwin (Exeter)
Claire Postlethwaite (Auckland)
Abstracts:
Yuri Bakhtin “Rare transitions in noisy heteroclinic networks”. We study white noise perturbations of planar dynamical systems with heteroclinic networks in the limit of vanishing noise. We show that the probabilities of transitions between various cells that the network tessellates the plane into decay as powers of the noise magnitude, and we describe the underlying mechanism. A metastability picture emerges, with a hierarchy of time scales and clusters of accessibility, similar to the classical Freidlin-Wentzell picture but with shorter transition times. We discuss applications of our results to homogenization problems and to the invariant distribution asymptotics. At the core of our results are local limit theorems for exit distributions obtained via methods of Malliavin calculus. Joint work with Hong-Bin Chen and Zsolt Pajor-Gyulai.
George Datseris “Methods and software for estimating basins of attraction of arbitrary dynamical systems”
Lauren Smith “Swarmalators with second order phase coupling: Syncing, swarming and clustering”. Coupled oscillators have been widely studied, with applications including brain and heart dynamics. Synchronisation is common to coupled oscillator networks, such that oscillators align temporally. Swarming behaviours have also been widely studied, such that independent agents aggregate spatially. For example, the flocking of birds or the schooling of fish. Here we consider a generalisation of the swarmalator model (O’Keeffe et al., Nat. Comm., 2017) in which particles termed “swarmalators” have both swarming spatial dynamics and oscillatory phase dynamics. A real-life example of swarmalators is sperm cells, whose oscillating tails create hydrodynamic forces that can lead to clustering. The swarmalator model has two-way coupling between the spatial and phase dynamics. The generalisation proposed here is to include the second harmonic in the phase coupling function. This yields many new phenomena, including anti-phase clustering, anti-phase segregation, and states with two large anti-phase clusters plus a small group of swarmalators that vacillate between them. Through mean-field reductions, critical sets of bifurcation parameters are analytically identified which agree with bifurcations observed in the full system.