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The effect of clustering on the Lotka-Volterra model. (English) Zbl 0671.34048

Summary: Using the Lotka-Volterra model as a reference for an oscillating system, the effects of nonideality, excluded volume and clustering, are investigated. It is found that these two different types of interaction have opposite effects on the stability of the system and that for a range of parameters stable limit cycles can result. Even limited clustering, such as dimer formation, is sufficient to give rise to limit-cycle behavior. Lattice models are also investigated where clustering is treated using the Bethe approximation.

MSC:

34D20 Stability of solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
92D25 Population dynamics (general)
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