# American Institute of Mathematical Sciences

2013, 2013(special): 663-672. doi: 10.3934/proc.2013.2013.663

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

 1 Lehrstuhl für Höhere Mathematik und Analytische Mechanik, Technische Universität München, Fakultät für Mathematik, D-85747 Garching, Germany

Received  August 2012 Revised  May 2013 Published  November 2013

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.
Citation: Florian Rupp, Jürgen Scheurle. Analysis of a mathematical model for jellyfish blooms and the cambric fish invasion. Conference Publications, 2013, 2013 (special) : 663-672. doi: 10.3934/proc.2013.2013.663
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