doi:10.1016/j.bulm.2004.03.005 Bulletin of Mathematical Biology (2004) 66, 1685–1704 An Analysis of a Nonlinear Stage-Structured Cannibalism Model with Application to the Northeast Arctic Cod Stock ARILD WIKAN ∗ Harstad University College, Havnegata 5, N-9480 Harstad, Norway E-mail: arild.wikan@hih.no ARNE EIDE Norwegian College of Fishery Science, University of Tromsø, Breivika, N-9037 Tromsø, Norway E-mail: arne@nfh.uit.no A two-dimensional stage-structured population model with nonlinear cannibalism terms is studied. We show that there is a large parameter interval where the non- trivial equilibrium of the model is the only stable attractor, but that there also exist parameter intervals where we find quasiperiodic, periodic and chaotic dynamics. Moreover, in the interplay between increasing the fecundity and increasing the can- nibalism pressure, the former turns out to be a destabilizing effect while the latter tends to act in a stabilizing fashion. Finally, we have applied the model to the North Atlantic cod stock using ICES biomass estimates. Our main conclusion from this study is that the combined effect of recruitment and cannibalism may not serve as an explanation of the observed fluctuations in the cod stock. c  2004 Society for Mathematical Biology. Published by Elsevier Ltd. All rights reserved. 1. I NTRODUCTION Several fish population biomasses of commercial interest show highly oscillatory year-to-year behavior; this is well documented in Myers et al. (1990) where data for several North Atlantic fish stocks during the period 1942–1987 are presented. Among them, the Barents Sea cod stock is known as a heavily fluctuating stock biomass (Ottersen, 1996). Periods of crises due to low availability of economically important fish species, in particular cod, have been documented in a number of sources over hundreds of years, as reviewed in the seminal work of Hjort (1914). ∗ Author to whom correspondence should be addressed. 0092-8240/04/061685 + 20 $30.00/0 c  2004 Society for Mathematical Biology. Published by Elsevier Ltd. All rights reserved.