Physics
Scientific paper
Oct 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007njph....9..378o&link_type=abstract
New Journal of Physics, Volume 9, Issue 10, pp. 378 (2007).
Physics
8
Scientific paper
In this paper, we consider instabilities of localized solutions in planar neural field firing rate models of Wilson Cowan or Amari type. Importantly we show that angular perturbations can destabilize spatially localized solutions. For a scalar model with Heaviside firing rate function, we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns.
With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem.
Coombes Stephen
Laing Carlo R.
Owen Michael R.
No associations
LandOfFree
Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1877859