A Simple Model of Periodic Reproduction: Selection of Prime Periods

  • Raul Abreu de AssisEmail author
  • Mazílio Coronel Malavazi
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 200)


A discrete-time model of periodic reproduction with inter and intra-specific competition is proposed as a tool to investigate the selection of prime reproduction cycle lengths, observed in certain species of cicadas. An approximation for the average populations is proposed and analyzed for the case of 2 and 13 populations. Results indicate that prime periods are in advantage when compared with composite ones, suggesting that the prime periods displayed by cicada species in nature might arise by the process of natural selection of adaptive values (and not as a random result of evolutionary constraints).


Difference equations Periodic reproduction Prime numbers Cicadas Magicicada 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Raul Abreu de Assis
    • 1
    Email author
  • Mazílio Coronel Malavazi
    • 2
  1. 1.Departamento de MatemáticaUNEMATSinopBrazil
  2. 2.Instituto de Ciências Naturais, Humanas e Sociais (ICNHS)—UFMTSinopBrazil

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