Patrick N McGraw

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We examine numerically the three-way relationships among structure, Laplacian spectra, and frequency synchronization dynamics on complex networks. We study the effects of clustering, degree distribution, and a particular type of coupling asymmetry (input normalization), all of which are known to have effects on the synchronizability of oscillator networks.(More)
By manipulating the clustering coefficient of a network without changing its degree distribution, we examine the effect of clustering on the synchronization of phase oscillators on networks with Poisson and scale-free degree distributions. For both types of networks, increased clustering hinders global synchronization as the network splits into dynamical(More)
We analyze the synchronization dynamics of phase oscillators far from the synchronization manifold, including the onset of synchronization on scale-free networks with low and high clustering coefficients. We use normal coordinates and corresponding time-averaged velocities derived from the Laplacian matrix, which reflects the network's topology. In terms of(More)
Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently random. In the oscillating state, signals propagate in a single direction and one or a few network loops are selected as(More)
We examine the large-network, low-loading behavior of an attractor neural network, the so-called bistable gradient network (BGN), and compare it with that of the Hopfield network (HN). We use analytical and numerical methods to characterize the attractor states of the network and their basins of attraction. The energy landscape of BGN is more complex than(More)
We outline a general theory for the analysis of flow-distributed standing and traveling wave patterns in one-dimensional, open flows of oscillatory chemical media, emphasizing features that are generic to a variety of kinetic models. We draw particular attention to the cases far from a Hopf bifurcation and far from the so-called kinematic or zero-diffusion(More)
We perform numerical studies of a reaction-diffusion system that is both Turing and Hopf unstable, and that grows by addition at a moving boundary (which is equivalent by a Galilean transformation to a reaction-diffusion-advection system with a fixed boundary and a uniform flow). We model the conditions of a recent set of experiments which used a temporally(More)
We examine numerically the storage capacity and the behavior near saturation of an attractor neural network consisting of bistable elements with an adjustable coupling strength, the bistable gradient network. For strong coupling, we find evidence of a first-order "memory blackout" phase transition, as in the Hopfield network. For weak coupling, on the other(More)
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