eprintid: 4226 rev_number: 6 eprint_status: archive userid: 351 dir: disk0/00/00/42/26 datestamp: 2016-01-15 02:05:01 lastmod: 2021-08-27 17:35:54 status_changed: 2016-01-15 02:05:01 type: article metadata_visibility: show item_issues_count: 1 creators_name: Ferriere, R. creators_name: Gatto, M. creators_id: 7498 creators_id: AL0683 title: Lyapunov exponents and the mathematics of invasion in oscillatory or chaotic populations ispublished: pub internal_subjects: iis_ecl divisions: prog_adn 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. date: 1995-10 date_type: published publisher: Elsevier id_number: 10.1006/tpbi.1995.1024 iiasapubid: XJ-95-119 iiasa_bibref: Theoretical Population Biology; 48(2):126-171 (October 1995) iiasa_bibnotes: [doi:10.1006/tpbi.1995.1024] creators_browse_id: 1248 creators_browse_id: 1897 full_text_status: none publication: Theoretical Population Biology volume: 48 number: 2 pagerange: 126-171 refereed: TRUE issn: 1096-0325 coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/article citation: Ferriere, R. & Gatto, M. (1995). Lyapunov exponents and the mathematics of invasion in oscillatory or chaotic populations. Theoretical Population Biology 48 (2) 126-171. 10.1006/tpbi.1995.1024 .