Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Comment: Is memristor a dynamic element?

The authors present a charge/flux formulation of the equations of memristive circuits, which seemingly show that the memristor should not be considered as a dynamic circuit element. Here, is shown that this approach implicitly reduces the dynamic analysis to a certain subset of the state space in such a way that the dynamic contribution of memristors is hidden. This reduction might entail a substantial loss of information, regarding e.g. the local stability properties of the circuit. Two examples illustrate this. It is concluded that the memristor, even with its unconventional features, must be considered as a dynamic element.

The anatomy of urban social networks and its implications in the searchability problem

The appearance of large geolocated communication datasets has recently increased our understanding of how social networks relate to their physical space. However, many recurrently reported properties, such as the spatial clustering of network communities, have not yet been systematically tested at different scales. In this work we analyze the social network structure of over 25 million phone users from three countries at three different scales: country, provinces and cities. We consistently find that this last urban scenario presents significant differences to common knowledge about social networks. First, the emergence of a giant component in the network seems to be controlled by whether or not the network spans over the entire urban border, almost independently of the population or geographic extension of the city. Second, urban communities are much less geographically clustered than expected. These two findings shed new light on the widely-studied searchability in self-organized networks. By exhaustive simulation of decentralized search strategies we conclude that urban networks are searchable not through geographical proximity as their country-wide counterparts, but through an homophily-driven community structure.