Related papers: Occupancy times for time-dependent stage-structure…
We examine to what extent the tempo and mode of environmental fluctuations matter for the growth of structured populations. The models are switching, linear ordinary differential equations $x'(t)=A(\sigma(\omega t))x(t)$ where…
This paper addresses the problem of learning instantaneous occupancy levels of dynamic environments and predicting future occupancy levels. Due to the complexity of most real-world environments, such as urban streets or crowded areas, the…
Models simulating household energy demand based on different occupant and household types and their behavioral patterns have received increasing attention over the last years due the need to better understand fundamental characteristics…
We consider the statistics of occupation times, the number of visits at the origin and the survival probability for a wide class of stochastic processes, which can be classified as renewal processes. We show that the distribution of these…
Occupation times quantify how long a stochastic process remains in a region, and their single-time statistics are famously given by the arcsine law for Brownian and L\'evy processes. By contrast, two-time occupation statistics, which…
To make informed decisions in natural environments that change over time, humans must update their beliefs as new observations are gathered. Studies exploring human inference as a dynamical process that unfolds in time have focused on…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
Mover-stayer models are used in social sciences and economics to model heterogeneous population dynamics in which some individuals never experience the event of interest ("stayers"), while others transition between states over time…
We investigate the statistics of the time taken for a system driven by recruitment to reach fixation. Our model describes a series of experiments where a population is confronted with two identical options, resulting in the system fixating…
In an introductory tutorial, we illustrated building cohort state-transition models (cSTMs) in R, where the state transitions probabilities were constant over time. However, in practice, many cSTMs require transitions, rewards, or both to…
We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly…
We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…
The theory of stationary spatially localized patterns in dissipative systems driven by time-independent forcing is well developed. With time-periodic forcing related but time-dependent structures may result. These may consist of breathing…
Failing to account for ecological processes such as dispersal and connectivity when modeling distributions can lead to biased inference about environmental drivers and reduced predictive performance. Spatial dynamic occupancy models are…
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…
In this paper, we prove a fluctuation theorem for the occupation time of the multi-species stirring process on a lattice starting from a stationary distribution. Our result shows that the occupation times of different species interact with…
Cyclic predator-prey models with four or six species are studied on a square lattice when the invasion rates are varied. It is found that the cyclic invasions maintain a self-organizing pattern as long as the deviation of the invasion…
We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one…