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This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the…
Accurate prediction of human or vehicle trajectories with good diversity that captures their stochastic nature is an essential task for many applications. However, many trajectory prediction models produce unreasonable trajectory samples…
We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two species, where one species has a more diverse diet than the…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
Climate changes may affect ecosystems destabilising relationships among species. We investigate the spatial rock-paper-scissors models with a regional unevenness that reduces the selection capacity of organisms of one species. Our results…
Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A…
Predicting species persistence within ecological communities is a fundamental challenge for both empirical and theoretical ecology. Existing methods span from mechanistic models, whose parameters are difficult to estimate from data, to…
Accurate and robust spatial orders are ubiquitous in living systems. In 1952, Alan Turing proposed an elegant mechanism for pattern formation based on spontaneous breaking of the spatial translational symmetry in the underlying…
Understanding the mechanisms that govern species coexistence and biodiversity represents a fundamental challenge in ecology. This study extends the classic rock-paper-scissors model by introducing a context-dependent higher-order…
MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs…
The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result.…
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…
How do seasonal successions influence the propagation dynamics of an age-structured invasive species? We investigate this problem by considering the scenario that the offsprings are reproduced in spring and then reach maturation in fall…
The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…
We investigate a tritrophic system in which organisms' energy depletion, resulting from failed selection attempts, leads to a partial loss of capacity to win the cyclic spatial game. The energy required to maintain optimal organism fitness…
This paper addresses an open inverse problem at the interface of mathematical analysis and spatial ecology: the unique identification of unknown spatial anomalies -- interpreted as zones of habitat degradation -- and their associated…
In many drylands around the globe, vegetation self-organizes into regular spatial patterns in response to aridity stress. We consider the regularly-spaced vegetation bands, on gentle hill-slopes, that survive low rainfall conditions by…
Antipredator behavior is present in many biological systems where individuals collectively react to an imminent attack. The antipredator response may influence spatial pattern formation and ecosystem stability but requires an organism's…
In this work, we consider the spatial-temporal multi-species competition model. A mathematical model is described by a coupled system of nonlinear diffusion-reaction equations. We use a finite volume approximation with semi-implicit time…