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Session S01 - Modeling and Computation for Control and Optimization of Biological and Physical Systems

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Mathematical model of a predator-prey food chain: plankton-anchovy

Neisser Pino Romero

Universidad Peruana Cayetano Heredia, Peru   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In the present work, a mathematical model is built that represents the dynamics that exist between phytoplankton (F), zooplankton (Z) and anchovy (A) from the model of Samares and Anal. This food chain occurs in the Peruvian maritime area where there is a three-link ecosystem, in addition to the fact that the food chain is a main axis in the ecological balance within the sea.

The behavior of the populations (maritime species) will be studied where the stability of the model (Routh-Hurwitz criterion) in the long term will be determined, where it will be complemented with the Dulac-Bendixon criterion for the state of coexistence of the three species.

Therefore, the dynamics of this food chain allows to have a fundamental axis in the economy and ecology for the country where it is sought to have a balance and stability of these two important activities. Without a doubt, the application of a model that helps us locate predation rates that do not disturb or affect ecological populations. This complication directly affects the ecosystem, especially because man is a predator that can lead to the extinction of the anchovy population and its upper chains. Consequently, this balance must be determined by the Peruvian Sea Institution (IMARPE) to maintain the biological balance.

Joint work with Christian Ulises Salazar Fernández (Universidad Nacional de Ingeniería, Perú).

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