Related papers: Dynamics of a diffusive competitive model on a per…
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model…
This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…
In this article, we focus on a doubly nonlinear nonlocal parabolic initial boundary value problem driven by the fractional $p$-Laplacian equipped with homogeneous Dirichlet boundary conditions on a domain in $\mathbb{R}^{d}$ and composed…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatial nonhomogeneous periodic solutions, which is induced by nonlocal…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and environmental driven changes on the marine ecosystem. In…
The co-optimization of a robot's body and brain presents a coupled challenge: the morphology constrains which control strategies are effective, while the control determines how well the morphology performs. To address this, we combine…
We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…
The influence of an external random field on the competition process in a nonlinear open spatially extended system is analyzed numerically. A three-component model is chosen as the competition model in which a "weak" species can move in…
The paper explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment. The harvesting effort is assumed to be proportional to the space-dependent intrinsic…
We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals…
The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…
This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…
Recent microbial experiments suggest that enhanced genetic drift at the frontier of a two-dimensional range expansion can cause genetic sectoring patterns with fractal domain boundaries. Here, we propose and analyze a simple model of…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
In this work, we study the dynamics of a spatially heterogeneous single population model with the memory effect and nonlinear boundary condition. By virtue of the implicit function theorem and Lyapunov-Schmidt reduction, spatially…
The paper presents a model of two-speed evolution in which the payoffs in the population game (or, alternatively, the individual preferences) slowly adjust to changes in the aggregate behavior of the population. The model investigates how,…
A microscopic agent dynamical model for diploid age-structured populations is used to study evolution of polymorphism and sympatric speciation. The underlying ecology is represented by a unimodal distribution of resources of some width.…