ACDC Seminar by Carlo Laing on June 16

On June 16 at 16:00, Carlo Laing will give an Amsterdam Dynamics Seminar. We will go for drinks at Bar Boele after the talk.

Title: 

The theta neuron is a simple model for the onset of periodic firing through a SNIC bifurcation. Infinite networks of theta neurons can be studied using the Ott/Antonsen ansatz, resulting in complex-valued Riccati equations that describe the macroscopic dynamics, in the form of a neural field model. Periodic solutions of these equations can be found self-consistently in a computationally efficient manner. We extend results from [1] to include the effects of distributed delays and conduction delays, finding and following periodic solutions in next generation neural field models. We concentrate on travelling waves, “breathing” bump states, and spatially uniform periodic states. We also determine the stability of stationary states as a function of delay parameters and find that most periodic solutions are created in Hopf bifurcations of these stationary states.

References

[1] C. R. Laing and O. E. Omel’chenko, Biological Cybernetics 117, 259–274, (2023)