Mathematical analysis of the navigational process in homing pigeons

In a novel approach based on the principles of dynamic systems theory, we analyzed the tracks of pigeons recorded with the help of miniaturized GPS recorders. Using the method of time lag embedding, we calculated the largest Lyapunov exponent to determine the system’s predictability and the correlation dimension to estimate the number of factors involved. A low Lyapunov exponent around 0.02, which proved to be rather constant over all calculations, indicates that the navigational process is almost deterministic. In the distribution of the correlation dimension estimates we found three distinctive peaks, at 3.3, 3.7 and 4.2, indicating that avian navigation is a complex multi-dimensional process, involving at least four or five independent factors. Additional factors, as indicated by an increase in the correlation dimension, seem to be included as the pigeons approach their home loft. This increase in correlation dimension and its fractal nature suggest that the various navigational factors can be included as required and weighted independently. Neither the correlation dimension nor the Lyapunov exponent is affected by increasing familiarity of the pigeons with the terrain. This suggests that the navigational strategy is stable with the same process controlling the flight across familiar as well as unfamiliar terrain.

► The navigational process of birds is almost deterministic.
► Avian navigation is a complex multi-dimensional process.
► The same process controls avian flight across familiar and unfamiliar terrain.
► Additional factors are included in the process as pigeons approach home.
► The navigational process of birds is flexible and additional factors can be included.