Bumps in small-world networks

11 Jul 2018, 12:00
New Law School/--101 (University of Sydney)

New Law School/--101

University of Sydney

Oral Presentation Minisymposium: Nonlocal models in biology Nonlocal models in biology


Carlo Laing (Massey University)


We consider a network of coupled excitatory and inhibitory theta neurons which is capable of supporting stable spatially-localised “bump” solutions. We randomly add long-range and simultaneously remove short-range connections within the network to form a small-world network and investigate the effects of this rewiring on the existence and stability of the bump solution. We consider two limits in which continuum equations can be derived; bump solutions are fixed points of these equations. We can thus use standard numerical bifurcation analysis to determine the stability of these bumps and to follow them as parameters (such as rewiring probabilities) are varied. We find that under some rewiring schemes bumps are quite robust, whereas in other schemes they can become unstable via Hopf bifurcation or even be destroyed in saddle-node bifurcations.

Primary author

Carlo Laing (Massey University)

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