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Large population limit and time behaviour of a stochastic particle model describing an age-structured population

Viet Chi Tran (2008)

ESAIM: Probability and Statistics


We study a continuous-time discrete population structured by a vector of ages. Individuals reproduce asexually, age and die. The death rate takes interactions into account. Adapting the approach of Fournier and Méléard, we show that in a large population limit, the microscopic process converges to the measure-valued solution of an equation that generalizes the McKendrick-Von Foerster and Gurtin-McCamy PDEs in demography. The large deviations associated with this convergence are studied. The upper-bound...

Large time behavior in a density-dependent population dynamics problem with age structure and child care

Vladas Skakauskas (2003)

Banach Center Publications

Two asexual density-dependent population dynamics models with age-dependence and child care are presented. One of them includes the random diffusion while in the other the population is assumed to be non-dispersing. The population consists of the young (under maternal care), juvenile, and adult classes. Death moduli of the juvenile and adult classes in both models are decomposed into the sum of two terms. The first presents death rate by the natural causes while the other describes the environmental...

Lévy Processes, Saltatory Foraging, and Superdiffusion

J. F. Burrow, P. D. Baxter, J. W. Pitchford (2008)

Mathematical Modelling of Natural Phenomena

It is well established that resource variability generated by spatial patchiness and turbulence is an important influence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulations indicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment can be formulated as a hitting time problem for a jump-diffusion process. We present two theoretical results. Firstly,...

Limitation and Regulation of Ecological Populations: a Meta-analysis of Tipula paludosa Field Data

R. P. Blackshaw, S. V. Petrovskii (2010)

Mathematical Modelling of Natural Phenomena

Whether the size of an animal population is environmentally limited or regulated by density dependent negative feedback mechanisms is of ecological interest. Proponents of limitation theory have issued a set of specific challenges which are addressed in this paper using field data for the insect Tipula paludosa. This species is known to be subject to population crashes caused by adverse environmental conditions and assumed to be limited. We re-examine published data in support of this hypothesis...

Local Collapses in the Truscott-Brindley Model

I. Siekmann, H. Malchow (2008)

Mathematical Modelling of Natural Phenomena

Relaxation oscillations are limit cycles with two clearly different time scales. In this article the spatio-temporal dynamics of a standard prey-predator system in the parameter region of relaxation oscillation is investigated. Both prey and predator population are distributed irregularly at a relatively high average level between a maximal and a minimal value. However, the slowly developing complex pattern exhibits a feature of “inverse excitability”: Both populations show collapses which occur...

Long-Time Simulation of a Size-Structured Population Model with a Dynamical Resource

L. M. Abia, O. Angulo, J. C. López-Marcos, M. A. López-Marcos (2010)

Mathematical Modelling of Natural Phenomena

In this paper, we study the numerical approximation of a size-structured population model whose dependency on the environment is managed by the evolution of a vital resource. We show that this is a difficult task: some numerical methods are not suitable for a long-time integration. We analyze the reasons for the failure.

Lotka-Volterra type predator-prey models: Comparison of hidden and explicit resources with a transmissible disease in the predator species

Luciana Assis, Malay Banerjee, Moiseis Cecconello, Ezio Venturino (2018)

Applications of Mathematics

The paper deals with two mathematical models of predator-prey type where a transmissible disease spreads among the predator species only. The proposed models are analyzed and compared in order to assess the influence of hidden and explicit alternative resource for predator. The analysis shows boundedness as well as local stability and transcritical bifurcations for equilibria of systems. Numerical simulations support our theoretical analysis.

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