Discrete Population Model for Fishery Stocks

This Demonstration displays the bifurcation diagram for a realistic population dynamic model given by , where is the intrinsic growth rate (taken here as a bifurcation parameter), is the number of fish (or density of population) at generation , and is the population capacity of the environment, set equal to 1 here. This mathematical expression was given by W. E. Ricker (1954), who invented a discrete population model for fishery stocks. The model can be used to predict the number of fish in a fishery. When the cycle of period three appears, . As expected, for higher values of , we observe chaotic behavior. Snapshots 2 to 5 present period three , period two , period four , and chaotic behaviors , respectively.


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[1] A. Varma and M. Morbidelli, Mathematical Methods in Chemical Engineering, New York: Oxford University Press, 1997.
[2] W. E. Ricker, "Stock and Recruitment," Journal of the Fisheries Research Board of Canada, 11(5), 1954 pp. 559–623. doi:10.1139/f54-039.
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