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A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption…
Cross-country soaring flights rely on intermittent atmospheric updrafts to cover long distances, producing trajectories that alternate between rapid relocation and local exploration. From a large dataset of paraglider, hang glider, and…
L\'{e}vy walk is a practical model and has wide applications in various fields. Here we focus on the effect of an external constant force on the L\'{e}vy walk with the exponent of the power-law distributed flight time $\alpha\in(0,2)$. We…
Motivated by a host of empirical evidences revealing the bursty character of human dynamics, we develop a model of human activity based on successive switching between an hesitation state and a decision-realization state, with residency…
We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics…
This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…
Edwards et al question aspects of the methods used in two of our published papers that report results showing Levy walk like and Levy flight movement patterns of marine predators.The criticisms are focused on the applicability of some…
This paper primarily investigates the geometric properties of excursions of L\'evy processes reflected at the past infimum with long lifetime or large height. For an oscillating process in the domain of attraction of a stable law, our…
Air transport systems are highly dynamic at temporal scales from minutes to years. This dynamic behavior not only characterizes the evolution of the system but also affect the system's functioning. Understanding the evolutionary mechanisms…
The actomyosin cortex is an active material that provides animal cells with a strong but flexible exterior, whose mechanics, including non-Gaussian fluctuations and occasional large displacements or cytoquakes, have defied explanation. We…
In the Heliosphere, power-law particle distributions are observed e.g. upstream of interplanetary shocks, which can result from superdiffusive transport. This non-Gaussian transport regime may result from intermittent magnetic field…
The random walk process in a nonhomogeneous medium, characterised by a L\'evy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is…
The L\'evy walk, a type of random walk characterized by linear step lengths that follow a power-law distribution, is observed in the migratory behaviors of various organisms, ranging from bacteria to humans. Notably, L\'evy walks with power…
We present a structured random-walk model that captures key aspects of how people communicate in groups. Our model takes the form of a correlated L\'{e}vy flight that quantifies the balance between focused discussion of an idea and…
Human mobility patterns are complex and distinct from one person to another. Nevertheless, motivated by tremendous potential benefits of modeling such patterns in enabling new mobile services and technologies, researchers have attempted to…
Understanding individual mobility behavior is critical for modeling urban transportation. It provides deeper insights on the generative mechanisms of human movements. Emerging data sources such as mobile phone call detail records, social…
As a significant factor in urban planning, traffic forecasting and prediction of epidemics, modeling patterns of human mobility draws intensive attention from researchers for decades. Power-law distribution and its variations are observed…
The success of collaboration between humans and robots in shared environments relies on the robot's real-time adaptation to human motion. Specifically, in Social Navigation, the agent should be close enough to assist but ready to back up to…
Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and humans in different situations are quite different. This paper proposes a general…
The L\'evy walk process for a lower interval of an excursion times distribution ($\alpha<1$) is discussed. The particle rests between the jumps and the waiting time is position-dependent. Two cases are considered: a rising and diminishing…