Prime number selection of cycles in a predator-prey model

Eric Goles, Oliver Schulz, Mario Markus

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


The fact that some species of cicadas appear every 7, 13, or 17 years and that these periods are prime numbers has been regarded as a coincidence. We found a simple evolutionary predator-prey model that yields prime-periodic preys having cycles predominantly around the observed values. An evolutionary game on a spatial array leads to travelling waves reminiscent of those observed in excitable systems. The model marks an encounter of two seemingly unrelated disciplines: biology and number theory. A restriction to the latter, provides an evolutionary generator of arbitrarily large prime numbers.

Original languageEnglish
Pages (from-to)33-38
Number of pages6
Issue number4
StatePublished - 2001
Externally publishedYes


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