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

Complementary action of chemical and electrical synapses to perception

Acknowledgements This study was possible by partial financial support from the following agencies: Fundação Araucária, EPSRC-EP/I032606/1, CNPq No. 441553/2014-1, CAPES No. 17656-12-5 and Science Without Borders Program— Process Nos. 17656125, 99999.010583/2013-00 and 245377/2012-3.Peer reviewedPostprin

Eclipse studies of the dwarf-nova Ex Draconis

We report on high speed photometry of EX Dra in quiescence and in outburst. The analysis of the lightcurves indicates that the outbursts do not start in the outer disc regions. The disc expands during rise to maximum and shrinks during decline and along the quiescent period. At the end of two outbursts the system was seen to go through a phase of lower brightness, characterized by an out-of-eclipse level ~15 per cent lower than the typical quiescent level and by the fairly symmetric eclipse of a compact source at disc centre with little evidence of a bright spot at disc rim. New eclipse timings were measured and a revised ephemeris was derived. The residuals with respect to the linear ephemeris are well described by a sinusoid of amplitude 1.2 minutes and period \~4 years and are possibly related to a solar-like magnetic activity cycle in the secondary star. Eclipse phases of the compact central source and of the bright spot were used to derive the geometry of the binary. By constraining the gas stream trajectory to pass through the observed position of the bright spot we find q=0.72+/-0.06 and i= 85 +3/-2 degrees. The binary parameters were estimated by combining the measured mass ratio with the assumption that the secondary star obeys an empirical main sequence mass-radius relation. We find M_1= 0.75+/-0.15 M_sun and M_2= 0.54+/-0.10 M_sun. The white dwarf at disc centre is surrounded by an extended and variable atmosphere or boundary layer of at least 3 times its radius and a temperature of T ~28000 K. The fluxes at mid-eclipse yield an upper limit to the contribution of the secondary star and lead to a lower limit photometric parallax distance of D= 290+/-80 pc. The fluxes of the secondary star are well matched by those of a M0+/-2 main sequence star.Comment: submitted to MNRAS, 12 pages, 9 figures; coded with MNRAS latex styl

V2051 Ophiuchi after superoutburst : out-of-plane material and the superhump light source

Aims. We performed a detailed spectroscopic analysis of the dwarf nova V2051 Oph at the end of its 1999 superoutburst. We studied and interpreted the simultaneous behaviour of various emission lines. Methods. We obtained high-resolution echelle spectroscopic data at ESO’s NTT with EMMI, covering the spectral range of 4000–7500 Å. The analysis was performed using standard IRAF tools. The indirect imaging technique of Doppler tomography was applied, in order to map the accretion disc and distinguish between the different emission sources. Results. The spectra are characterised by strong Balmer emission, together with lines of He i and the iron triplet Fe ii 42. All lines are double-peaked, but the blue-to-red peak strength and central absorption depth vary. The primary’s velocity was found to be 84.9 kms−1. The spectrograms of the emission lines reveal the prograde rotation of a disc-like emitting region and, for the Balmer and He i lines, an enhancement of the red-wing during eclipse indicates a bright spot origin. The modulation of the double-peak separation shows a highly asymmetric disc with non-uniform emissivity. This is confirmed by the Doppler maps, which apart from the disc and bright spot emission also indicate an additional region of enhanced emission in the 4th quadrant (+Vx, −Vy), which we associate with the superhump light source. Given the behaviour of the iron triplet and its distinct differences from the rest of the lines, we attribute its existence to an extended gas region above the disc. Its origin can be explained through the fluorescence mechanism

Mathematical model of brain tumour with glia-neuron interactions and chemotherapy treatment

Acknowledgements This study was possible by partial financial support from the following Brazilian government agencies: Fundação Araucária, EPSRC-EP/I032606/1 and CNPq, CAPES and Science Without Borders Program Process nos. 17656125, 99999.010583/2013-00 and 245377/2012-3.Peer reviewedPreprin