We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. Focusing on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone, we compare the synchronization properties of static and fluctuating networks in the regime of large delays. We find that random network switching may enhance the stability of synchronized states. Synchronization appears to be maximally stable when fluctuations are much faster than the time-delay, whereas it disappears for very slow fluctuations. For fluctuation time scales of the order of the time-delay, we report a resynchronizing effect in finite-size networks. Moreover, we observe characteristic oscillations in all regimes, with a periodicity related to the time-delay, as the system approaches or drifts away from the synchronized state.

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Background Biosecurity is known as the implementation of measures to reduce the risk of introduction (external biosecurity) and spread (internal biosecurity) of disease agents. One of the most common diseases in the porcine industry is the porcine reproductive and respiratory syndrome (PRRS), which has a huge negative impact on the well-being of the animals and consequently, on their productivity. Nonetheless, most of the biosecurity evaluation tools are based on scored systems. A new digital biosecurity system was designed to help control PRRS virus (PRRSv) infection status throughout an objective tool for the evaluation of internal biosecurity based on a system of control of the flow of internal movement of personnel in commercial farms. Movements, routes and health data were combined to classify the staff movements into three categories including “Risky” (From PCR(+) to PCR(-) barns), “Unsafe” (between PCR(+) barns) and “Safe” (From PCR(-)). Therefore, the main aims of the present work were to evaluate the efficacy of this new tool, its relationship with PRRSv incidence as well as to demonstrate the importance of biosecurity education to help farm workers to adopt safer daily practices. Results The observed results showed an overall smaller number of monthly movements (p < 0.05) and a significant increase in the Safe movements percentage (p < 0.05), concomitant with a decrease in the Risky movements percentage (p < 0.05) after the training session. In regards the relationship between staff movements and PRRSv presence, neither the percentage nor the total amount of both Safe and Unsafe movements were significantly different between the PCR(+) and PCR(-) groups of PRRSv status (p > 0.05). Nonetheless, both the total number and the percentage of Risky movements were significantly lower in the PCR(-) group (p < 0.05) compared with PCR(+) group. These results show a clear relationship between the total amount of Risky movements and the probability of a PRRSv outbreak in the farms. Conclusions Our results support the notion that staff movement patterns within the different farm areas are a major factor in its internal biosecurity. The new tool described in the current work showed a significant relationship between staff movements and the probability of PRRSv outbreak and demonstrate the importance of biosecurity training to help farm workers adopt safer daily practices.

An individual's social group may be represented by their ego-network, formed by the links between the individual and their acquaintances. Ego-networks present an internal structure of increasingly large nested layers of decreasing relationship intensity, whose size exhibits a precise scaling ratio. Starting from the notion of limited social bandwidth, and assuming fixed costs for the links in each layer, we propose a grand-canonical ensemble that generates the observed hierarchical social structure. This result suggests that, if we assume the existence of layers demanding different amounts of resources, the observed internal structure of ego-networks is indeed a natural outcome to expect. In the thermodynamic limit, realized when the number of ego-network copies is large, the specific layer degrees reduce to Poisson variables. We also find that, under certain conditions, equispaced layer costs are necessary to obtain a constant group size scaling. Finally, we fit and compare the model with an empirical social network.

In this communication we present some of our recent results on the synchronization properties of directed delay-coupled networks of a small-world type, whose topology changes with time. Our simulations of a network of non-linear elements show that a random change of topology enhances the stability of a synchronized state, depending on the interplay between different timescales in the dynamics. The results are analytically explained in the linear limit, where the dynamics is expressed in terms of an effective connectivity matrix. In the limit of fast network fluctuations, this effective connectivity is given by the arithmetic mean of the temporal adjacency matrices. When the coupling topology changes slowly, the effective adjacency matrix is given by the geometric mean. The transition between both regimes is numerically studied for linear network elements.