Influence of local carrying capacity restrictions on stochastic predator-prey models

We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained for site-restricted model variants. In accord with the classic Lotka-Volterra mean-field description, both species always coexist in two dimensions. Yet competing activity fronts generate complex, correlated spatio-temporal structures. As a consequence, finite systems display transient erratic population oscillations with characteristic frequencies that are renormalized by fluctuations. For large reaction rates, when the processes are rendered more local, these oscillations are suppressed. In contrast with site-restricted predator-prey model, we observe species coexistence also in one dimension. In addition, we report results on the steady-state prey age distribution.Comment: Latex, IOP style, 17 pages, 9 figures included, related movies available at http://www.phys.vt.edu/~tauber/PredatorPrey/movies

Selected topics on reaction-diffusion-advection models from spatial ecology

We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments. Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplankton growth, and spatial spread of epidemic disease. Open problems and conjectures are presented

Dynamic Peer-to-Peer Competition

The dynamic behavior of a multiagent system in which the agent size $s_{i}$ is variable it is studied along a Lotka-Volterra approach. The agent size has hereby for meaning the fraction of a given market that an agent is able to capture (market share). A Lotka-Volterra system of equations for prey-predator problems is considered, the competition factor being related to the difference in size between the agents in a one-on-one competition. This mechanism introduces a natural self-organized dynamic competition among agents. In the competition factor, a parameter $\sigma$ is introduced for scaling the intensity of agent size similarity, which varies in each iteration cycle. The fixed points of this system are analytically found and their stability analyzed for small systems (with $n=5$ agents). We have found that different scenarios are possible, from chaotic to non-chaotic motion with cluster formation as function of the $\sigma$ parameter and depending on the initial conditions imposed to the system. The present contribution aim is to show how a realistic though minimalist nonlinear dynamics model can be used to describe market competition (companies, brokers, decision makers) among other opinion maker communities.Comment: 17 pages, 50 references, 6 figures, 1 tabl

Dynamics of nonautonomous eco-pidemiological models

We consider a general eco-epidemiological model which includes a large variety of eco-epidemiological models available in the literature. We assume that the parameters are time dependent and we consider general functions for the predation on infected and uninfected prey and also for the vital dynamics of uninfected prey and predator populations. We studied this model in four scenarios: non-autonomous, periodic, discrete and random. In the non-autonomous and discrete case we discussed the uniform strong persistence and extinction of the disease, in the periodic case, we studied the existence of an endemic periodic orbit, and nally, in the random case we studied the existence of random global attractors.Nesta tese consideramos um modelo eco-epidemiológico geral que inclui uma grande variedade de modelos eco-epidemiológicos presentes na literatura. Assumimos que os parâmetros dependem do tempo e consideramos funções gerais para a predação de presas infectadas e não infectadas e também para a dinâmica vital de presas não infectadas e da população de predadores. Estudamos estes modelos em quatro cenários: não-autónomo geral, periódico, discreto e aleatório. Nos casos não-autónomo geral e discreto analisamos a persistência forte e extinção da doença, no caso periódico estudamos as condições para a existência de uma órbita periódica endémica e, finalmente, no caso aleatório estudamos a existência de atratores globais aleatórios