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Recent increase in wildfires worldwide has led to the need for real-time fire nowcasting. Physics-driven models, such as cellular automata and computational fluid dynamics can provide high-fidelity fire spread simulations but they are…
We consider a forest-fire model which, somewhat informally, is described as follows: Each site (vertex) of the square lattice is either vacant or occupied by a tree.Vacant sites become occupied at rate 1. Further, each site is hit by…
Place one active particle at the root of a graph and a Poisson-distributed number of dormant particles at the other vertices. Active particles perform simple random walk. Once the number of visits to a site reaches a random threshold, any…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
In the thermodynamic limit, a probabilistic cellular automaton can be approximated by a deterministic nonlinear map. Here we construct such a map for the forest fire problem. The construction is based on the results of the Monte Carlo…
We propose a discrete two-dimensional mathematical model for forest fires and we derive certain results describing its limiting behavior. We also pose a relevant open question.
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced…
This article explores the dynamics of savanna ecosystems with grazing, browsing, and migration effects. Covering over one-eighth of the Earth's land area and supporting about one-fifth of the global population, the savanna is an ecological…
Computational models for understanding and predicting fire in wildland and managed lands are increasing in impact. Data characterizing the fuels and environment is needed to continue improvement in the fidelity and reliability of fire…
Observed bimodal tree cover distributions at particular environmental conditions and theoretical models indicate that some areas in the tropics can be in either of the alternative stable vegetation states forest or savanna. However, when…
In many data scientific problems, we are interested in inferring causal relationships in the data generating mechanism. Here, we consider the following real-world question: how has the Colombian conflict influenced tropical forest loss?…
We study finite-size effects in the self-organized critical forest-fire model by numerically evaluating the tree density and the fire size distribution. The results show that this model does not display the finite-size scaling seen in…
Forest transitions, characterized by dynamic shifts between forest, agricultural, and abandoned lands, are complex phenomena. This study developed a stochastic differential equation model to capture the intricate dynamics of these…
The minimal ecological requirements for formation of regular vegetation patterns in semiarid systems have been recently questioned. Against the general belief that a combination of facilitative and competitive interactions is necessary,…
Based on complex network theory, we propose a computational methodology that addresses the spatial distribution of fuel breaks for the inhibition of the spread and size of wildland fires on heterogeneous landscapes. This is a two-tire…
Vegetation in semi-arid environments self-organizes into striking spatial patterns -- bands, spots, labyrinths, and gaps -- with characteristic wavelengths on the order of tens to hundreds of meters. Existing reaction-diffusion models…
Ecological communities exhibit pervasive patterns and inter-relationships between size, abundance, and the availability of resources. We use scaling ideas to develop a unified, model-independent framework for understanding the distribution…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
Recently, large-scale cascading failures in complex systems have garnered substantial attention. Such extreme events have been treated as an integral part of the self-organized criticality (SOC). Recent empirical work has suggested that…