To address the collective motion of swimming organisms encapsulated in a droplet, an active-hydrodynamic framework is constructed for assemblies contractile swimmers inside binary-fluid droplet. At low activity, this yields self-propelling droplet whose center mass (CM) displays rectilinear motion. With increasing CM L\'evy-walk-type super-diffusive motion, and interface exhibits multifractal f...

The apparent fractal properties of TCP data tra c have recently attracted con siderable interest Most prominently fractional Brownian motion FBM has been used to model the long range dependence of tra c traces through self similarity Tra c being by nature a process of positive increments though a multifractal ap proach appears more natural In this study various traces of TCP tra c have been ana...

Abstract: These lectures notes aim at introducing Lévy processes in an informal and intuitive way, accessible to non-specialists in the field. In the first part, we focus on the theory of Lévy processes. We analyze a ‘toy’ example of a Lévy process, viz. a Lévy jump-diffusion, which yet offers significant insight into the distributional and path structure of a Lévy process. Then, we present sev...

Article history: Lévy flights represent the best strategy to randomly search for a target in an unknown environment, and have been widely observed in many animal species. Here, we inspect and discuss recent results concerning human behavior and cognition. Different studies have shown that human mobility can be described in terms of Lévy flights, while fresh evidence indicates that the same patt...

The diffusion entropy analysis measures the scaling of the probability density function (pdf) of the diffusion process generated by time series imagined as a physical source of fluctuations. The pdf scaling exponent, δ, departs in the non-Gaussian case from the scaling exponent HV evaluated by variance based methods. When δ = 1/(3 − 2HV ) Lévy statistics characterizes the time series. With the ...

This work is to investigate the (top) Lyapunov exponent for a class of Hamiltonian systems under small non-Gaussian L\'evy noise. In suitable moving frame, linearisation such system can be regarded as perturbation nilpotent linear system. The then estimated by taking Pinsky-Wihstutz transformation and applying Khas'minskii formula, appropriate assumptions on smoothness, ergodicity integrability...

In this paper we study two properties of the numerical solutions a controlled stochastic Lotka-Volterra one-predator-two-prey model, namely boundedness in mean and strong convergence these solutions. We also establish solve, by means Stochastic Maximum Principle, corresponding optimal control problem population modeled system with types environmental fluctuations: white noise L´evy jumps. Our s...

The apparent`fractal' properties of TCP data traac have recently attracted considerable interest. Most prominently, fractional Brownian motion (FBM) has been used to model the long range dependence of traac traces through self-similarity. Traac being by nature a process of positive increments, though, a multifractal approach appears more natural. In this study, various traces of TCP traac have ...