An introduction to cicada periodic evolution models
DOI:
https://doi.org/10.17268/sel.mat.2021.02.04Keywords:
Discrete models, systems with delay, periodic solution, synchronized emergencyAbstract
A remarkable feature of some insects is the synchronized emergence of a large number of insects, such as cicadas that appear in bud ratios every 13 to 17 years. Therefore, this paper presents several mathematical models that explain such synchronized evolutions for certain life cycles in the cicada. For this purpose, a discrete model with lags, proposed by Hoppensteadt and Keller, is taken as a reference, where the population for a type of cicada incorporates a predator species and a carrying capacity in the environment. A qualitative analysis of this system is carried out to determine the existence of synchronized solutions, and the results are contrasted with other models.
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