Wilten Nicola, Sue Ann CampbellWe study large networks of Wilson-Cowan neural field systems with homeostatic plasticity. These networks have been known to display rich dynamical states such consisting of a single recurrently coupled, or two cross-coupled nodes [1]. These dynamics include chaos, mixed mode oscillations and chaos, and synchronized chaos, even under these simple connectivity profiles in small networks. Here, we consider these networks with connectomes that display so- called L1 normalization, but are otherwise arbitrary under large network limits. We find that for the majority of classical connectomes considered (Random, Small World), the network displays a large-scale chaotic synchronization to the attractor states and bifurcation sequence of a single recurrently coupled node as in [1]. However, connectomes that display sufficiently large pairs of eigenvalues can trigger multiple Hopf bifurcations which can potentially collide in Torus bifurcations that can destabilize the synchronized, single node attractor solutions. Our analysis demonstrates that for Wilson-Cowan systems with Homeostatic plasticity, the dominant determinant of network activity is not the connectome directly, but rather the connectome's ability to generate large eigenvalues that can induce multiple nearby Hopf bifurcations. If the connectome cannot generate these large pairs of eigenvalues, the dynamics of the network considered become limited to the dynamics of a single recurrently coupled node. [1] Nicola, W., Hellyer, P. J., Campbell, S. A., & Clopath, C. (2018). Chaos in homeostatically regulated neural systems. _Chaos: An Interdisciplinary Journal of Nonlinear Science_ , _28_ (8), 083104.
