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Analysis of a mathematical model for jellyfish blooms and the cambric fish invasion

Pages: 663 - 672, Issue special, November 2013

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Florian Rupp - Lehrstuhl für Höhere Mathematik und Analytische Mechanik, Technische Universität München, Fakultät für Mathematik, D-85747 Garching, Germany (email)
Jürgen Scheurle - Lehrstuhl für Höhere Mathematik und Analytische Mechanik, Technische Universität München, Fakultät für Mathematik, D-85747 Garching, Germany (email)

Abstract: Dramatic increases in jellyfish populations which lead to the collapse of formerly healthy ecosystems are repeatedly reported from many different sites, cf. [6,8,14]. Due to their devastating effects on fishery the understanding of the causes for such a blooming are of major ecological as well as economical importance. Assuming fish as the dominant predator species we model a combined two species system subject to constant environmental conditions. By totally analytic means we completely classify all biologically relevant equilibria in terms of existence and Lyapunov stability, and give a complete description of this system's non-linear global dynamics supported by numerical simulations. This approach complements, from a systematic point of view, the studies given in the literature to better understand jellyfish blooms.

Keywords:  Population dynamics, stability, bifurcation.
Mathematics Subject Classification:  Primary: 37N25, 37G10, 37G15, 37C75; Secondary: 34Cxx.

Received: August 2012;      Revised: May 2013;      Published: November 2013.

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