«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «BIOLOGIYA. ECOLOGIYA»
«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «BIOLOGY. ECOLOGY»
ISSN 2073-3372 (Print)

List of issues > Series «Biology. Ecology». 2016. Vol. 15

Degradation of Commercial Fish Stocks: Experience of Mathematical Modeling (on the Example of Northern Cod)

Author(s)
A. Yu. Perevaryukha
Abstract

We consider the situation with the sharp decline in atlantic cod Gadus morhua stocks off the coast of Canada in 1992. By using data on catches of cod we identified a number of universal features of the dynamics of unexpected degradation in terms of the nonlinear dynamics. Computational models such nonsmooth development process, we succeeded implement based on the analysis of the main principles of the theory of the formation of the replenishment of fish. The model is based on the formalization of the changing generation of fish survival. As an additional option in the second equation we takes into account the growth rate of juvenile fish. A discrete-continuous dynamic system describes the long emerging transition a prosperous population from a steady state with a high number of individuals after the increase in the proportion of commercial exemptions to the aperiodic fluctuations at low density of fish. The countdown biological resources degradation is implemented in a scenario as a boundary crisis of the interval attracting set as the boundary of the domain of attraction of the attractor is a small, existing for a low number range, slightly removed from the critical point. After the first fall of the fish population and without a moratorium on fishing for such fluctuations are moving rapidly into a state where supplies are not restored from the second crisis, which confirms example of the whitefish of Lake Ontario.

Keywords
nonlinear model of populations, depletion of fish stocks, northern cod collapse
UDC
639.215.2

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