17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper MoP10.2

Townley, Stuart (Univ. of Exeter), Hodgson, David (Univ. of Exeter), McCarthy, Dominic (Univ. of Exeter)

Robustness Tools for Stage-Structured Population Dynamics

Scheduled for presentation during the Regular Session "Biological Systems" (MoP10), Monday, July 24, 2006, 15:45−16:10, Room 103

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on March 28, 2024

Keywords Uncertain systems, Biological systems analysis

Abstract

Our motivation for this paper is two fold: Matrix models from Ecology are frequently used in systems theory as examples of non-negative sytems -- in robustness, in input output theory, in switched systems; In modern ecology, a fundamental task is to assess the effect that perturbations to life-cycle transition rates of individuals have on population dynamics, leading to harvesting and conservation (i.e. control).

Whilst there is a significant commonality of concepts and issues between `control theory' for non-negative systems and population dynamics in ecology, the gap between the two is quite significant. Indeed, on the one hand population ecology has not embraced recent developments in control theory especially the tools from robust control. On the other hand, whilst non-negativity arising in ecological models is frequently used as motivation for theoretical problems in control theory, many other related issues of equal importance are often over-looked. These include boundedness constraints on system parameters and also the specific nature of structured perturbations which result from the underlying biology. We attempt to bridge this gap between systems theory and matrix modelling in population ecology. We focus on a number of application-specific perturbation problems and show how they can be formulated and analysed using robustness methodologies.