Multifractal Analysis Of Animal Trajectories

The multifractal problem of two-dimensional directed walk has always been a topic of interest in the fractal community.Pigeon homing is a kind of directed walk that exists in nature.There are currently two directed walk models,one is the model of birds navigating along a straight line,and the other is the two-dimensional directed random walk model.However,neither of these two models can guarantee that the pigeons can return to the target point smoothly.This thesis proposes a strict directed walk based on the bird navigation with compass proposed by the predecessors.It conforms to the characteristics of pigeon homing,and can ensure that the pigeon flies in the direction of the target and can accurately return to the target point.It is called the pigeon homing model.The simulation generated 5000 trajectories and averaged them.It is found that the trajectories generated by the pigeon homing model have multifractal behavior.Up to now,most of the studies have used some index to describe the shape characteristics of animal trajectories.After the introduction of mono-fractal,it only calculates the fractal dimensions of the trajectories,and does not conduct a detailed analysis of the fractal natures of the motion trajectories.Using fractal dimension to analyze the shape of animal trajectory has two flaws,and may ignore the potential multifractal.This thesis analyzes the multifractal nature of the actual flight trajectory of the pigeons.First,calculate some indicators describing the shape of the flight path of the pigeons,and found that there are contradictions between the results obtained by different indicators,which proves that the straightness index and other indicators describing the shape characteristics of the animal's movement trajectories have flaws.Then use detrend fluctuation analysis and detrend cross-correlation analysis to calculate the detrend crosscorrelation coefficients of the pigeons' flight trajectories,and explore the crosscorrelation within their trajectories.It is found that there is a cross-correlation between the two coordinate sequences of these trajectories.Then the multifractal methods are introduced into the analysis of animal motion trajectories to study the multifractal characteristics.Use multifractal detrend fluctuation analysis and multifractal detrend cross-correlation analysis methods to explore the multifractal characteristics of the actual flight trajectory of pigeons.It can be seen from the calculated results that the actual flight trajectory of pigeons have multifractal natures.The two coordinate sequences x sequence and y sequence of the pigeon flight trajectories have autocorrelation behavior,and the autocorrelation behavior is multifractal and continuous,and there is cross-correlation behavior between the two coordinate sequences,and the cross-correlation behavior is also multifractal and continuous.This is consistent with the conclusion that the trajectories generated by the pigeon homing model has multifractal behavior.