Variance-mediated multifractal analysis of group participation in chasing a single dangerous prey

Complexity of group participation in chasing a single dangerous prey is usually influenced by many factors such as the group size, the physiological fitness of predator, the hunting tactics and the running speed of prey. The group members may take diversified roles and switch their roles in the process of group hunting. In this paper, we study group participation in lions' pride hunting by using a minimal cheating-pursuing model formulated in discrete-time random walks. Predator's switching between cheating state and pursuing state is determined by a preset probability transition matrix which is regarded to be a product of the combination of various factors that influence group participation. The physiological constraints of lions require that the measurement of complexity of group participation must be built for short time series. On the basis of 300 simulated time steps, numerical results show that our model reasonably reflects the common expectation that the pride groups tightly in chasing a single slow prey while in chasing a single fast prey it groups loosely. We compute the distance between the group center and the center of the concerted pursuing for the quantification of group participation. Complexity embedded in short time series of these quantities is measured via a new method named variance-mediated multifractal analysis. This method is based on the partition function which is the weighted sum of probability measures of qth power. The short time series is divided into non-overlapping windows where the sample variance of each window is used to build the normalized probability measure. A strategy, “one-point indent for local past”, is designed to weigh the probability measures. The singularity spectrum exhibits more multifractality in the simulated group participation in chasing a fast prey and far less such in chasing a slow one, showing the potential applications of this method in studying short process of group hunting.