Pattern Formation by Boundary Forcing in Convectively Unstable, Oscillatory Media With and Without Differential Transport

Motivated by recent experiments and models of biological segmentation, we analyze the exicitation of pattern-forming instabilities of convectively unstable reaction-diffusion-advection (RDA) systems, occuring by means of constant or periodic forcing at the upstream boundary. Such boundary-controlled pattern selection is a generalization of the flow-distributed oscillation (FDO) mechanism that can include Turing or differential flow instability (DIFI) modes. Our goal is to clarify the relationships among these mechanisms in the general case where there is differential flow as well as differential diffusion. We do so by analyzing the dispersion relation for linear perturbations and showing how its solutions are affected by differential transport. We find a close relationship between DIFI and FDO, while the Turing mechanism gives rise to a distinct set of unstable modes. Finally, we illustrate the relevance of the dispersion relations using nonlinear simulations and we discuss the experimental implications of our results.Comment: Revised version with added content (new section and figures added), changes to wording and organizatio

Flow distributed oscillation, flow velocity modulation and resonance

We examine the effects of a periodically varying flow velocity on the standing and travelling wave patterns formed by the flow-distributed oscillation (FDO) mechanism. In the kinematic (or diffusionless) limit, the phase fronts undergo a simple, spatiotemporally periodic longitudinal displacement. On the other hand, when the diffusion is significant, periodic modulation of the velocity can disrupt the wave pattern, giving rise in the downstream region to travelling waves whose frequency is a rational multiple of the velocity perturbation frequency. We observe frequency locking at ratios of 1:1, 2:1 and 3:1, depending on the amplitude and frequency of the velocity modulation. This phenomenon can be viewed as a novel, rather subtle type of resonant forcing.Comment: submitted to Phys. Rev.

Analysis of Nonlinear Synchronization Dynamics of Oscillator Networks by Laplacian Spectral Methods

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 these coordinates, synchronization manifests itself as a contraction of the dynamics onto progressively lower-dimensional submanifolds of phase space spanned by Laplacian eigenvectors with lower eigenvalues. Differences between high and low clustering networks can be correlated with features of the Laplacian spectrum. For example, the inhibition of full synchoronization at high clustering is associated with a group of low-lying modes that fail to lock even at strong coupling, while the advanced partial synchronizationat low coupling noted elsewhere is associated with high-eigenvalue modes.Comment: Revised version: References added, introduction rewritten, additional minor changes for clarit

Clustering and Synchronization of Oscillator Networks

Using a recently described technique for 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 network, increased clustering hinders global synchronization as the network splits into dynamical clusters that oscillate at different frequencies. Surprisingly, in scale-free networks, clustering promotes the synchronization of the most connected nodes (hubs) even though it inhibits global synchronization. As a result, scale-free networks show an additional, advanced transition instead of a single synchronization threshold. This cluster-enhanced synchronization of hubs may be relevant to the brain with its scale-free and highly clustered structure.Comment: Submitted to Phys. Rev.

Bistable Gradient Networks II: Storage Capacity and Behaviour Near Saturation

We examine numerically the storage capacity and the behaviour near saturation of an attractor neural network consisting of bistable elements with an adjustable coupling strength, the Bistable Gradient Network (BGN). 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 hand, there is no evidence of such a transition and memorized patterns can be stable even at high levels of loading. The enhanced storage capacity comes, however, at the cost of imperfect retrieval of the patterns from corrupted versions.Comment: 15 pages, 12 eps figures. Submitted to Phys. Rev. E. Sequel to cond-mat/020356

Topology and Computational Performance of Attractor Neural Networks

To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world and scale-free topologies. The random net is the most efficient for storage and retrieval of patterns by the entire network. However, in the scale-free case retrieval errors are not distributed uniformly: the portion of a pattern encoded by the subset of highly connected nodes is more robust and efficiently recognized than the rest of the pattern. The scale-free network thus achieves a very strong partial recognition. Implications for brain function and social dynamics are suggestive.Comment: 2 figures included. Submitted to Phys. Rev. Letter

Colouration in amphibians as a reflection of nutritional status : the case of tree frogs in Costa Rica

Colouration has been considered a cue for mating success in many species; ornaments in males often are related to carotenoid mobilization towards feathers and/or skin and can signal general health and nutrition status. However, there are several factors that can also link with status, such as physiological blood parameters and body condition, but there is not substantial evidence which supports the existence of these relationships and interactions in anurans. This study evaluated how body score and blood values interact with colouration in free-range Agalychnis callidryas and Agalychnis annae males. We found significant associations between body condition and plasmatic proteins and haematocrit, as well as between body condition and colour values from the chromaticity diagram. We also demonstrated that there is a significant relation between the glucose and plasmatic protein values that were reflected in the ventral colours of the animals, and haematocrit inversely affected most of those colour values. Significant differences were found between species as well as between populations of A. callidryas, suggesting that despite colour variation, there are also biochemical differences within animals from the same species located in different regions. These data provide information on underlying factors for colouration of male tree frogs in nature, provide insights about the dynamics of several nutrients in the amphibian model and how this could affect the reproductive output of the animals