Optimal network topologies for information transmission in active networks

This work clarifies the relation between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how to determine a network topology that is optimal for information transmission. By optimal, we mean that the network is able to transmit a large amount of information, it possesses a large number of communication channels, and it is robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.Comment: 20 pages, 12 figure

Network Mutual Information and Synchronization under Time Transformations

We investigate the effect of general time transformations on the phase synchronization (PS) phenomenon and the mutual information rate (MIR) between pairs of nodes in dynamical networks. We demonstrate two important results concerning the invariance of both PS and the MIR. Under time transformations PS can neither be introduced nor destroyed and the MIR cannot be raised from zero. On the other hand, for proper time transformations the timing between the cycles of the coupled oscillators can be largely improved. Finally, we discuss the relevance of our findings for communication in dynamical networks.Comment: 15 p

Sensitive Dependence on Parameters of Continuous-time Nonlinear Dynamical Systems

We would like to thank the partial support of this work by the Brazilian agencies FAPESP (processes: 2011/19296-1 and 2013/26598-0, CNPq and CAPES. MSB acknowledges EPSRC Ref. EP/I032606/1.Peer reviewedPostprin

Experimental observation of a complex periodic window

The existence of a special periodic window in the two-dimensional parameter space of an experimental Chua's circuit is reported. One of the main reasons that makes such a window special is that the observation of one implies that other similar periodic windows must exist for other parameter values. However, such a window has never been experimentally observed, since its size in parameter space decreases exponentially with the period of the periodic attractor. This property imposes clear limitations for its experimental detection.Comment: 4.2 pages, 4 figure

Characterization in bi-parameter space of a non-ideal oscillator

The authors thank scientific agencies CAPES, CNPq (112952/2015-1), and FAPESP (2011/ 19269-11). M. S. Baptista also thanks EPSRC (EP/I03 2606/1).Peer reviewedPostprin

A spiral structure in the disk of EX Draconis on the rise to outburst maximum

We report on the R-band eclipse mapping analysis of high-speed photometry of the dwarf nova EX Dra on the rise to the maximum of the November 1995 outburst. The eclipse map shows a one-armed spiral structure of ~180 degrees in azimuth, extending in radius from R ~0.2 to 0.43 R_{L1} (where R_{L1} is the distance from the disk center to the inner Lagrangian point), that contributes about 22 per cent of the total flux of the eclipse map. The spiral structure is stationary in a reference frame co-rotating with the binary and is stable for a timescale of at least 5 binary orbits. The comparison of the eclipse maps on the rise and in quiescence suggests that the outbursts of EX Dra may be driven by episodes of enhanced mass-transfer from the secondary star. Possible explanations for the nature of the spiral structure are discussed.Comment: To appear in the Astrophysical Journal Letters; 8 pages, 2 figures; coded with AAS latex styl