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August  2001, 1(3): 387-399. doi: 10.3934/dcdsb.2001.1.387

The prime number periodical cicada problem

G.F. Webb 1,

1. 

Department of Mathematics, Vanderbilt University, Nashville, TN 37340

Received  December 1999 Revised  April 2000 Published  May 2001

Mathematical models are presented to argue for the significance of prime number emergences of 13 year and 17 year periodical cicadas (Magicicada spp.). The prime number values arise as resonances of emergences with 2 and 3 year quasi-cycling predators. Predators with 2 and 3 year quasi-cycles are present due to their age dependent fecundity and mortality rates. Their quasi-cycles are enhanced by the predation of cicadas during emergences and thus exert significant influence on the cicada periodic life cycles.
Keywords: age-structured population., Periodic emergences, discrete time difference equation.
Mathematics Subject Classification: 92D2.
Citation: G.F. Webb. The prime number periodical cicada problem. Discrete & Continuous Dynamical Systems - B, 2001, 1 (3) : 387-399. doi: 10.3934/dcdsb.2001.1.387
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