Schieber, T.A.; Carpi, L.; Frery, A.; Rosso, O. A.; Pardalos, P.M.; Ravetti, M.G Physics letters A Vol. 380, num. 3, p. 359-364 DOI: 10.1016/j.physleta.2015.10.055 Data de publicació: 2016-01-28 Article en revista
A crucial challenge in network theory is the study of the robustness of a network when facing a sequence of failures. In this work, we propose a dynamical definition of network robustness based on Information Theory, that considers measurements of the structural changes caused by failures of the network's components. Failures are defined here as a temporal process defined in a sequence. Robustness is then evaluated by measuring dissimilarities between topologies after each time step of the sequence, providing a dynamical information about the topological damage. We thoroughly analyze the efficiency of the method in capturing small perturbations by considering different probability distributions on networks. In particular, we find that distributions based on distances are more consistent in capturing network structural deviations, as better reflect the consequences of the failures. Theoretical examples and real networks are used to study the performance of this methodology.
The multifractal character of the daily extreme temperatures in Catalonia (NE Spain) is analyzed by means of the multifractal detrended fluctuation analysis (MF-DFA) applied to 65 thermometric records covering years 1950–2004. Although no clear spatial patterns of the multifractal spectrum parameters appear, factor scores deduced from Principal Component analysis indicate some signs of spatial gradients. Additionally, the daily extreme temperature series are classified depending on their complex time behavior, through four multifractal parameters (Hurst exponent, Hölder exponent with maximum spectrum, spectrum asymmetry and spectrum width). As a synthesis of the three last parameters, a basic measure of complexity is proposed through a normalized Complexity Index. Its regional behavior is found to be free of geographical dependences. This index represents a new step towards the description of the daily extreme temperatures complexity.
We study the regime of anticipated synchronization in unidirectionally coupled chaotic maps such that the slave map has its own output re-injected after a certain delay. For a class of simple maps, we give analytic conditions for the stability of the synchronized solution, and present results of numerical simulations of coupled 1D Bernoulli-like maps and 2D Baker maps, that agree well with the analytic predictions.
We find families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton properties.
The new Lorenz system of general circulation of the atmosphere, which exhibits an immense variety of bifurcation sequences, is studied by computer simulation. When the external heating varies, periodic and turbulent regions are found. In the periodic regions, period-doubling, period-halving and saddle-node bifurcations are observed. Also, at certain parameter intervals, hysteresis and coexistence of attractors is reported. The chaotic behavior in the turbulent region is discussed with the aid of Lyapunov analysis and correlation dimension calculations.