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arXiv · 2502.18048

Stability of oscillations in the spatially extended May-Leonard model

Idan Sorin·Alexander Nepomnyashchy·Vladimir Volpert
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Abstract

The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their stability with respect to spatially periodic disturbances is studied. The stability of solu tions with respect to longwave spatial modulations is revealed. A period doubling instability breaking the spatial uniformity is found.

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Idan Sorin, Alexander Nepomnyashchy, Vladimir Volpert. 2025-02-25. Stability of oscillations in the spatially extended May-Leonard model. https://doi.org/10.1137/25m1737201

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