𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Structured Population Models, Conservation Laws, and Delay Equations

✍ Scribed by G. Bocharov; K.P. Hadeler

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
193 KB
Volume
168
Category
Article
ISSN
0022-0396

No coin nor oath required. For personal study only.

✦ Synopsis

dedicated to professor jack k. hale on the occasion of his 70th birthday

The general principles by which certain structured population models or renewal equations can be reduced to ordinary differential equations or delay equations are systematically investigated with particular attention to retarded and neutral delay differential equations. Approriate state spaces are defined and their relations are studied, as well as the positivity of the resulting evolutionary systems. 2000

πŸ“œ SIMILAR VOLUMES

The Application of Mass and Energy Conse
The Application of Mass and Energy Conservation Laws in Physiologically Structured Population Models of Heterotrophic Organisms
✍ S.A.L.M. Kooijman; B.W. Kooi; T.G. Hallam πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 259 KB

Rules for energy uptake, and subsequent utilization, form the basis of population dynamics and, therefore, explain the dynamics of the ecosystem structure in terms of changes in standing crops and size distributions of individuals. Mass fluxes are concomitant with energy flows and delineate function

Norm conservation for generalized kineti
Norm conservation for generalized kinetic population models with delay
✍ M. Bodnar πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 840 KB

## In this paper, the problem of Lr-norm conservation for generalized Boltzmann models with delay is presented. Conditions which guarantee conservation of L'-norm are proved in the case of linear and bilinear equation. Examples when the norm is not conserved and some numerical results are presente

Conservation laws for Lotka–Volterra mod
Conservation laws for Lotka–Volterra models
✍ Rainer Schimming πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 110 KB

## Abstract We derive necessary and sufficient conditions on a Lotka–Volterra model to admit a conservation law of Volterra's type. The result and the proof for the corresponding linear algebra problem are given in graph‐theoretical terms; they refer to the directed graph which is defined by the co

Boundedness for impulsive delay differen
Boundedness for impulsive delay differential equations and applications to population growth models
✍ Xinzhi Liu; George Ballinger πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 244 KB

In this paper, criteria on uniform ultimate boundedness are derived for impulsive delay di erential equations using Lyapunov functions and Razumikhin techniques. It should be noted that the boundedness criteria establish global existence of solutions as well as boundedness without assuming, a priori