SYNCHRONIZATION OF 2-CYCLES FOR THREE MIGRATION – CONNECTED POPULATIONS

I.G. Sukhodoev

Аннотация


The work deals with investigation of the oscillation synchronization in a system of three populations, migration – related in a ring. The dynamics model represents a system of three identical logistic dissipatively interconnected mappings. The author has constructed a complete phase portrait of the model using qualitative methods of dynamic systems study. It is shown that there are several periodic points in the phase space, corresponding to synchronous and asynchronous cycles.


Ключевые слова


population; migration; cycles; synchronization; phase portrait; bifurcation

Литература


REFERENCE: Sukhodoev I.G. Synchronization of 2-cycles for three migration – connected populations. Regional’nye problemy, 2024, vol. 27, no. 3, pp. 5–7. (In Russ.). DOI: 10.31433/2618-9593-2024-27-3-5-7.

Sukhodoev I.G., Kulakov M.P., Kurilova E.V., Frisman E.Ya. Features of synchronization of dynamics in a system of three migration-related populations. Regional’nye problemy, 2024, vol. 27, no. 1, pp. 50–61. (In Russ.). DOI: 10.31433/2618-9593-20224-27-1-50-61.

Kulakov M.P., Aksenovich T.I., Frisman E.Ya. Approaches to describing the spatial dynamics of migration-related populations: analysis of cycle synchronization. Regional’nye problemy, 2013, vol. 16, no. 1, pp. 5–15. (In Russ.).

Earn D.J.D., Rohani P., Grenfell B.T. Persistence, chaos and synchrony in ecology and epidemiology. Proceedings of the Royal Society of London. Series B: Biological Sciences, 1998, vol. 265, no. 1390, pp. 7–10. DOI: 10.1098/rspb.1998.0256.

England J.P., Krauskopf B., Osinga H.M. Computing One-Dimensional Stable Manifolds and Stable Sets of Planar Maps without the Inverse. SIAM Journal on Applied Dynamical Systems, 2004, vol. 3, no. 2, pp. 161–190. DOI: 10.1137/030600131.


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