Geodesic
Local dynamics of a pair of Hutchinson equations with competitive and diffusion coupling
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 155-162

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In this paper, we study the dynamics of a system consisting of two coupled Hutchinson equations taking into account the competitive and diffusion coupling between populations. A local asymptotic analysis of the system is performed in the case where the coupling coefficients are small and the parameters of the oscillators are close to the values that provide the Andronov–Hopf bifurcation. We also examine the scenario of phase rearrangements of the system under a change in the diffusion parameter and analyze the dependence of this scenario on the coefficient of competition coupling.
Keywords: Hutchinson equation, competitive coupling, method of normal forms, asymptotics, stability.
Mots-clés : diffusion coupling 
@article{INTO_2021_194_a13,
     author = {E. A. Marushkina and E. S. Samsonova},
     title = {Local dynamics of a pair of {Hutchinson} equations with competitive and diffusion coupling},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {155--162},
     publisher = {mathdoc},
     volume = {194},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_194_a13/}
}
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E. A. Marushkina; E. S. Samsonova. Local dynamics of a pair of Hutchinson equations with competitive and diffusion coupling. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 155-162. http://geodesic.mathdoc.fr/item/INTO_2021_194_a13/