PREY-PREDATOR TRIDIAGONAL LOTKA-VOLTERRA MODELS

Andrey Antonov, Svetoslav Nenov, Tzvetelin Tzvetkov

Abstract


The prey-predator Lotka-Volterra models are some of the mostpopular mathematical models in biology and chemistry. Usually, these mod-els are the first tool used to analyze cooperativity, oscillatory behavior, andspaces synchronization at large scale of biochemistry, bio-molecular, and med-ical interaction models. These properties are in relationship with existence offirst integrals and stability behavior of the systems. Especially, and maybe themost essential results are related to existence (or non-existence) of boundedand periodic orbits.

In this paper we determine a family of independent first integrals, criteria forexistence of bounded orbits, and stability criteria for a family of n-dimensionalLotka-Volterra systems, generated by periodic tridiagonal matrices.


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