Lyapunov exponents and the mathematics of invasion in oscillatory or chaotic populations

Ferriere R & Gatto M (1995). Lyapunov exponents and the mathematics of invasion in oscillatory or chaotic populations. Theoretical Population Biology 48 (2): 126-171. DOI:10.1006/tpbi.1995.1024.

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Abstract

This paper concisely reviews the mathematical properties of the dominant Lyapunov exponent of a matrix sequence in the context of population biology. The concept of Lyapunov exponent provides a valuable tool for investigating processes of invasion in ecology or genetics, which are crucial in shaping community diversity, determining the spread of epidemics or the fixation of a new mutation. The appeal of the invasibility criterion based on the dominant Lyapunov exponent lies in the opportunity it offers to deal with population structure, complex life cycles, and complex population dynamics resulting from the model nonlinearities (oscillations, chaos), as well as random fluctuations arising from a stochastic environment. We put emphasis on the issues of the existence, numerical approximation, and regularity of the dominant Lyapunov exponent. Our presentation is aimed at showing that, despite our inability to compute the exponent analytically, which adds to its high intrinsic instability, important biological insights can nevertheless be achieved at the cost of fairly mild assumptions on the features of the models considered.

Item Type: Article
Research Programs: Adaptive Dynamics Network (ADN)
Bibliographic Reference: Theoretical Population Biology; 48(2):126-171 (October 1995)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:05
Last Modified: 25 Feb 2016 09:28
URI: http://pure.iiasa.ac.at/4226

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