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Feedback and Robustness in Population Dynamics

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If you have a question about this talk, please contact Dr Guy-Bart Stan.

The familiar control systems notions of feedback, parameter uncertainty and robustness are highly relevant in biological and ecological processes. So the usual small gain theorems and stability criteria ought to be very useful. However, in the case of biological applications, other aspects such as positive systems and monotonicity also come in to play. In this talk we will focus on two examples: Density dependence (nonlinearity) in models of endangered plants and parametric uncertainty in generic population projection models (PPMs). Within this framework of positive systems, we use small gain type theorems to establish existence of GAS equilibria in the plant models and a simple characterisation of growth rates to characterise the growth-decline boundary for PPMs. The talk is based on joint work with the Control Theory – Math Biology collaboration at the University of Nebraska (Richard Rebarber, Brigitte Tenhumberg).

This talk is part of the CUED Control Group Seminars series.

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