Related papers: Space use by foragers consuming renewable resource…
This paper presents a detailed characterization of the trajectory of a single housefly with free range of a square cage. The trajectory of the fly was recorded and transformed into a time series, which was fully analyzed using an…
We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
Aging refers to the property of two-time correlation functions to decay very slowly on (at least) two time scales. This phenomenon has gained recent attention due to experimental observations of the history dependent relaxation behavior in…
In drylands, water availability determines plant population densities and whether they cooperate via facilitation or compete. When water scarcity intensifies, plant densities decrease and competition for water surpasses the benefits of soil…
Branching random flights are key to describing the evolution of many physical and biological systems, ranging from neutron multiplication to gene mutations. When their paths evolve in bounded regions, we establish a relation between the…
Local interactions, when individuals meet, can regulate collective behavior. In a system without any central control, the rate of interaction may depend simply on how the individuals move around. But interactions could in turn influence…
Overpopulation and environmental degradation due to inadequate resource-use are outcomes of human's ecosystem engineering that has profoundly modified the world's landscape. Despite the age-old concern that unchecked population and economic…
In legged locomotion, the relationship between different gait behaviors and energy consumption must consider the full-body dynamics and the robot control as a whole, which cannot be captured by simple models. This work studies the robot…
Be $X_t$ a random walk. We study its span $S$, i.e. the size of the domain visited up to time $t$. We want to know the probability that $S$ reaches $1$ for the first time, as well as the density of the span given $t$. Analytical results are…
Genetic information and environmental factors determine the path of an individuals life and therefore, the evolution of its entire species. We have succeeded in proposing and studying a model that captures this idea. In our model, a…
Mechanistic home range models are important tools in modeling animal dynamics in spatially-complex environments. We introduce a class of stochastic models for animal movement in a habitat of varying preference. Such models interpolate…
Flocking is a paradigmatic example of collective animal behaviour, where decentralized interaction rules give rise to a globally ordered state. In the emergence of order out of self-organization we find similarities between biological…
How do social animals make effective decisions in the absence of a leader? While coordination can improve accuracy, it also introduces delays as information propagates through the group. In changing environments, these delays can outweigh…
We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…
The most profound change in the relationship between humans and their environment was the introduction of agriculture and pastoralism. [....] For an understanding of the expansion process, it appears appropriate to apply a diffusive model.…
We introduce random walks in a sparse random environment on $\mathbb Z$ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent…
Soaring birds gain energy from stable ascending currents or shear. However, it remains unclear whether energy loss due to drag can be overcome by extracting work from transient turbulent fluctuations. We designed numerical simulations of…
Information theory has explained the organization of many biological phenomena, from the physiology of sensory receptive fields to the variability of certain DNA sequence ensembles. Some scholars have proposed that information should…
This thesis explores a central question: how does memory affect the way random walkers explore space? By analyzing various non-Markovian models, where past behavior directly influences future dynamics, we uncover new mechanisms and…