Centenary of the first predator-prey model. Revision, modifications and challenges of this fundamental ecological interrelationship
DOI:
https://doi.org/10.17268/sel.mat.2025.02.16Keywords:
Predator-prey model, refuge, stability, bifurcations, limit cycles, separatrix curvesAbstract
For many applied mathematicians, and especially for biomathematicians, the first model proposed by the Italian mathematician Vito Volterra in 1926 is well known, describing for the first time the relationship between a predator and its prey. This model coincided with a similar system, on chemical reactions, proposed by the physicist-chemist Alfred J. Lotka years earlier. Since then, and with an epidemic character, variations, modifications, and the incorporation of new phenomena or ecological principles have been formulated to ”make more realistic” the foundations and studies on this fundamental interaction between two species of living beings. In this work, we will give a brief description of the historical context of this seminal model, emphasizing its main properties; then we will add specific modifications, briefly outlining properties of some of them.
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