Article:
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F. Rupp & J. Scheurle (2013): Analysis of a Mathematical Model for Jellyfish
Blooms and the Cambric Fish Invasion, Dynamical Systems and Differential
Equations, DCDS Supplement 2013 Proceedings of the 9th AIMS International
Conference (Orlando, USA), pp. 663-672.


Abstract:
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Dramatic increases in jellyfish populations which lead to the collapse of
formerly healthy ecosystems are repeatedly reported from many different sites,
cf. [a], [a], [c]. 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.



Cited sources in the abstract:
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[a]  M. Kawahara, S. Uye, K. Ohtsu, and H. Iizumi, Unusual population explosion
     of the giant jellyfish nemopilema nomurai (scyphozoa: rhizostomeae) in
     east asian waters, Marine Ecology Progress Series, 307 (2006), pp. 161-173.
[b]  C.E. Mills, Jellyfish blooms: are populations increasing globally in
     response to changing ocean conditions?, Hydrobiologia, 451 (2001), 55–68.
[c]  A.J. Richardson, A. Bakun, G.C. Hays, and M.J. Gibbons, The jellyfish
     joyride: causes, consequences and management responses to a more gelatinous
     future, Trends in Ecology and Evolution, 24 (2009), 312–322.