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For a Nicholson's blowflies system with patch structure and multiple discrete delays, we analyze several features of the global asymptotic behavior of its solutions. It is shown that if the spectral bound of the community matrix is…
Multiple-scale mobility is ubiquitous in nature and has become instrumental for understanding and modeling animal foraging behavior. However, the impact of individual movements on the long-term stability of populations remains largely…
This paper studies the Lotka-Volterra competition model with cross-diffusion terms under homogeneous Dirichlet boundary conditions. We consider the asymptotic behavior of positive steady-states as equal two cross-diffusion coefficients tend…
Uncovering structural properties of ecological networks is a crucial starting point of studying the system's stability in response to various types of perturbations. We analyze pollination and seed disposal networks, which are…
The maintenance of diversity, the `commonness of rarity', and compositional turnover are ubiquitous features of species-rich communities. Through a minimal model, we consider how these features reflect the interplay between environmental…
Mutualistic networks have attracted increasing attention in the ecological literature in the last decades as they play a key role in the maintenance of biodiversity. Here, we develop an analytical framework to study the structural stability…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
We study the stability of $\mathcal{M}_0$, an invariant subset of a Markov process $(X_t)_{t\geq 0}$ on a metric space $\mathcal{M}$. By building the theory of average Lyapunov functions, we formulate general criteria based on the signs of…
We study an individual-based predator-prey model of biological coevolution, using linear stability analysis and large-scale kinetic Monte Carlo simulations. The model exhibits approximate 1/f noise in diversity and population-size…
Understanding the architectural subtleties of ecological networks, believed to confer them enhanced stability and robustness, is a subject of outmost relevance. Mutualistic interactions have been profusely studied and their corresponding…
Ecological communities are composed of species interactions that respond to environmental fluctuations. Despite increasing evidence of temporal variation in these interactions, most theoretical frameworks remain rooted in static…
A mutualism is an interaction where the involved species benefit from each other. We study a two-dimensional hexagonal three-state cellular automaton model of a two-species mutualistic system. The simple model is characterized by four…
The generalized Lotka-Volterra (GLV) equations with quenched random interactions have been extensively used to investigate the stability and dynamics of complex ecosystems. However, the standard linear interaction model suffers from…
We introduce a minimalistic model based on dynamic node deletion and node duplication with heterodimerisation. The model is intended to capture the essential features of the evolution of protein interaction networks. We derive an exact…
Microbial ecosystems are remarkably diverse, stable, and often consist of a balanced mixture of core and peripheral species. Here we propose a conceptual model exhibiting all these emergent properties in quantitative agreement with real…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
In natural ecosystems, species can be characterized by the nonlinear density-dependent self-regulation of their growth profile. Species of many taxa show a substantial density-dependent reduction for low population size. Nevertheless, many…
We analyze the long term behavior of interacting populations which can be controlled through harvesting. The dynamics is assumed to be discrete in time and stochastic due to the effect of environmental fluctuations. We present extinction…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…
Transitions to absorbing states are of fundamental importance in non-equilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three…