Related papers: Scaling and Intermittency in Animal Behavior
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…
The Levy-flight dynamics can stem from simple random walks in a system whose operational time (number of steps n) typically grows superlinearly with physical time t. Thus, this processes is a kind of continuous-time random walks (CTRW),…
Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce randomly distributed resources, but a less explored alternative is that this behaviour may result from the…
Recent experiments (G. Ariel, et al., Nature Comm. 6, 8396 (2015)) revealed an intriguing behavior of swarming bacteria: they fundamentally change their collective motion from simple diffusion into a superdiffusive L\'{e}vy walk dynamics.…
The study of animal movement is challenging because it is a process modulated by many factors acting at different spatial and temporal scales. Several models have been proposed which differ primarily in the temporal conceptualization,…
Turbulent winds and gusts fluctuate on a wide range of timescales from milliseconds to minutes and longer, a range that overlaps the timescales of avian flight behavior, yet the importance of turbulence to avian behavior is unclear. By…
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation by animals and also in human mobility. One way to create such regimes are L\'evy flights, where the walkers…
Recent studies have shown that the spatial structures of animal displacements and local-scale human motion follow L\'{e}vy flights. Whether transnational human activity (THA) also exhibits such a pattern has however not been thoroughly…
Levy walk is a fundamental model with applications ranging from quantum physics to paths of animal foraging. Taking animal foraging as an example, a natural idea that comes to one's mind is to introduce the multiple internal states for…
Martensites subjected to quasistatic deformation are known to exhibit power law distributed acoustic emission in a broad range of scales, however, the origin of the observed scaling behavior and the mechanism of self-organization towards…
The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations…
Anomalous diffusion, manifest as a nonlinear temporal evolution of the position mean square displacement, and/or non-Gaussian features of the position statistics, is prevalent in biological transport processes. Likewise, collective behavior…
On-off intermittency occurs in nonequilibrium physical systems close to bifurcation points and is characterised by an aperiodic switching between a large-amplitude "on" state and a small-amplitude "off" state. L\'evy on-off intermittency is…
Stochastic resetting is a protocol of starting anew, which can be used to facilitate the escape kinetics. We demonstrate that restarting can accelerate the escape kinetics from a finite interval restricted by two absorbing boundaries also…
L\'evy walks are random walk processes whose step-lengths follow a long-tailed power-law distribution. Due to their abundance as movement patterns of biological organisms, significant theoretical efforts have been devoted to identifying the…
We study Markovian continuous-time random walk models for L\'evy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal to zero in…
The time evolution of random variables with L\'evy statistics has the ability to develop jumps, displaying very different behaviors from continuously fluctuating cases. Such patterns appear in an ever broadening range of examples including…
The existence of power-law distributions is only a first requirement in the validation of the critical behavior of a system. Long-range spatio-temporal correlations are fundamental for the spontaneous neuronal activity to be the expression…