Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force

We identify a novel route to the birth of a strange nonchaotic attractor (SNA) in a quasiperiodically forced electronic circuit with a nonsinusoidal (square wave) force as one of the quasiperiodic forces through numerical and experimental studies. We find that bubbles appear in the strands of the quasiperiodic attractor due to the instability induced by the additional square wave type force. The bubbles then enlarge and get increasingly wrinkled as a function of the control parameter. Finally, the bubbles get extremely wrinkled (while the remaining parts of the strands of the torus remain largely unaffected) resulting in the birth of the SNA which we term as the \emph{bubbling route to SNA}. We characterize and confirm this birth from both experimental and numerical data by maximal Lyapunov exponents and their variance, Poincar\'e maps, Fourier amplitude spectra and spectral distribution function. We also strongly confirm the birth of SNA via the bubbling route by the distribution of the finite-time Lyapunov exponents.Comment: 11 pages. 11 figures, Accepted for publication in Phys. Rev.

Honeybee navigation: distance estimation in the third dimension

Honeybees determine distance flown by gauging the extent to which the image of the environment moves in the eye as they fly towards their goal. Here we investigate how this visual odometer operates when a bee flies along paths that include a vertical component. By training bees to fly to a feeder along tunnels of various three-dimensional configurations, we find that the odometric signal depends only upon the total distance travelled along the path and is independent of its three-dimensional configuration. Hence, unlike walking desert ants, which measure the distance travelled in the horizontal plane whilst traversing undulating terrain, flying bees simply integrate the image motion that is experienced on the way to the goal, irrespective of the direction in which the image moves across the eyes. These findings raise important questions about how honeybee recruits navigate reliably to find the food sources that are advertised by scouts

Large Array Channel Capacity in the Presence of Interference

We develop a model for a large array ground receiver system for use in deep-space communications, and analyze the resulting array channel capacity. The model includes effects of array geometry, time-dependent spacecraft orbital trajectory, point and extended interference sources, and elevation-dependent noise and tropospheric channel variations. Channel capacity is expressed as the ratio of determinants of covariance matrices characterizing source, interference, and additive noise, and then reduced to a simpler quadratic form more amenable to analysis and numerical computation. This formulation facilitates inclusion of array and channel characteristics into the model, as well as comparison of optimal, suboptimal, and equivalent single antenna configurations on achievable throughput. Realistic examples of ground array channel capacity calculations are presented, demonstrating the impact of array geometry, planetary interference sources, and array combining algorithm design upon the achievable data throughput