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We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…
A model of the mechanisms underlying exploratory behaviour, based on empirical research and refined using a computer simulation, is presented. The behaviour of killifish from two lakes, one with killifish predators and one without, was…
In this paper we consider the 2-component reaction-diffusion model that was recently obtained by a systematic reduction of the 3-component Gilad et al. model for dryland ecosystem dynamics. The nonlinear structure of this model is more…
We study a driven zero range process which models a closed system of attractive particles that hop with site-dependent rates and whose steady state shows a condensation transition with increasing density. We characterise the dynamical…
We study a model of flocking in order to describe the transitions during the collective motion of organisms in three dimensions (e.g., birds). In this model the particles representing the organisms are self-propelled, i.e., they move with…
Artificially evolving foraging behavior in simulated legged animals has proved to be a notoriously difficult task. Here, we co-evolve the morphology and controller for virtual organisms in a three-dimensional physically realistic…
We study the evolution of a pathogen with two allelic types infecting a population of hosts, where within-host type frequencies evolve in discrete time. Our framework is built on a two-parameter family of transition kernels on [0,1], which…
Elephant random walk is a special type of random walk that incorporates the memory of the past to determine its future steps. The probability of this walk taking a particular step (+1 or -1) at a time point, conditioned on the entire…
In this paper, we consider the state-dependent reflecting random walk on a half-strip. We provide explicit criteria for (positive) recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed…
Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…
This paper deals with a new class of random flights $\underline{\bf X}_d(t),t>0,$ defined in the real space $\mathbb{R}^d, d\geq 2,$ characterized by non-uniform probability distributions on the multidimensional sphere. These random motions…
Path integration enables desert arthropods to find back to their nest on the shortest track from any position. To perform path integration successfully, speeds and turning angles along the preceding outbound path have to be measured…
This book chapter introduces to the problem to which extent search strategies of foraging biological organisms can be identified by statistical data analysis and mathematical modeling. A famous paradigm in this field is the Levy Flight…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of…
Time series observations are ubiquitous in astronomy, and are generated to distinguish between different types of supernovae, to detect and characterize extrasolar planets and to classify variable stars. These time series are usually…
In the current paper Fokker Planck model of random walks has been extended to non conservative cases characterized by explicit dependence of diffusion and energy on time. A given generalization allows describing of such non equilibrium…
Quantifying and comparing patterns of dynamical ecological systems require averaging over measurable quantities. For example, to infer variation in movement and behavior, metrics such as step length and velocity are averaged over large…
Damselflies show abrupt, darting flight, which is the envy of aero-engineers. This amazing ability is used both to capture prey and, by males, to establish territories that can attract females. In this work, high-resolution, high-speed…