Related papers: A modified chemostat exhibiting competitive exclus…
This paper is framed in a series of studies on attraction-repulsion chemotaxis models combining different effects: nonlinear diffusion and sensitivities and logistic sources, for the dynamics of the cell density, and consumption and/or…
Neoclassical economics has two theories of competition between profit-maximizing firms (Marshallian and Cournot-Nash) that start from different premises about the degree of strategic interaction between firms, yet reach the same result,…
Modern ecology has re-emphasized the need for a quantitative understanding of the original 'survival of the fittest theme' based on analyzis of the intricate trade-offs between competing evolutionary strategies that characterize the…
We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…
Persistent economic competition is often justified as a mechanism of innovation, efficiency, and welfare maximization. Yet empirical evidence across disciplines reveals that competition systematically generates fragility, inequality, and…
Explaining how competing species coexist remains a central question in ecology. The well-known competitive exclusion principle (CEP) states that two species competing for the same resource cannot stably coexist, and more generally, that the…
As early indicated by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of…
Conventional wisdom suggests that environmental noise drives populations toward extinction. In contrast, we report a paradoxical phenomenon in which stochasticity reverses a deterministic tipping point, thereby preventing collapse. Using a…
Linking the microscopic and macroscopic behavior is at the heart of many natural and social sciences. This apparent similarity conceals essential differences across disciplines: while physical particles are assumed to optimize the global…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
Cyclic dominant systems, like rock-paper-scissors game, are frequently used to explain biodiversity in nature, where mobility, reproduction and intransitive competition are on stage to provide the coexistence of competitors. A significantly…
We present properties of Lotka-Volterra equations describing ecological competition among a large number of competing species. First we extend to the case of a non-homogeneous niche space stability conditions for solutions representing…
In this thesis we use dynamical systems to analize the consequences of competition in the arrival of a foreign species in an ecosystem.
In this paper we present and analyse a simple two populations model with migrations among two different environments. The populations interact by competing for resources. Equilibria are investigated. A proof for the boundedness of the…
We investigate the controllability of the competition-diffusion Lotka-Volterra system. Our primary focus is on the one-dimensional setting with Dirichlet boundary controls, interpreted as ecological management policies regulating the…
A central goal in ecology is to understand how biodiversity is maintained. Previous theoretical works have employed the rock-paper-scissors (RPS) game as a toy model, demonstrating that population mobility is crucial in determining the…
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…
We investigate the problem of the predominance and survival of "weak" species in the context of the simplest generalization of the spatial stochastic rock-paper-scissors model to four species by considering models in which one, two, or…
Ecosystems dynamics is often considered as driven by a coupling of species' resource consumption and its population size dynamics. Such resource-population dynamics is captured by MacArthur-type models. One biologically relevant feature…
A discrete chemotactic predator-prey model is proposed in which the prey secrets a diffusing chemical which is sensed by the predator and vice versa. Two dynamical states corresponding to catching and escaping are identified and it is shown…