Hopf bifurcation for a class of predator-prey system with small immigration

Mauricio F. S. Lima; Jaume Llibre

doi:10.3934/ERA.2024209

Hopf bifurcation for a class of predator-prey system with small immigration

Mauricio F. S. Lima, Jaume Llibre

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Resum

The subject of this paper concerns with the bifurcation of limit cycles for a predator-prey model with small immigration. Since, in general, the biological systems are not isolated, taking into account immigration in the model becomes more realistic. In this context, we deal with a model with a Holling type I function response and study, using averaging theory of second order, the Hopf bifurcation that can emerge under small perturbation of the biological parameters.

Idioma original	Anglès
Pàgines (de-a)	4604-4613
Nombre de pàgines	10
Revista	Electronic Research Announcements of the American Mathematical Society
Volum	32
Número	7
DOIs	https://doi.org/10.3934/ERA.2024209
Estat de la publicació	Publicada - 26 de jul. 2024

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10.3934/ERA.2024209

https://ddd.uab.cat/record/303171

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title = "Hopf bifurcation for a class of predator-prey system with small immigration",

abstract = "The subject of this paper concerns with the bifurcation of limit cycles for a predator-prey model with small immigration. Since, in general, the biological systems are not isolated, taking into account immigration in the model becomes more realistic. In this context, we deal with a model with a Holling type I function response and study, using averaging theory of second order, the Hopf bifurcation that can emerge under small perturbation of the biological parameters.",

keywords = "Hopf bifurcation, averaging equation, limit cycle, periodic orbit, predator-prey system",

author = "Lima, \{Mauricio F. S.\} and Jaume Llibre",

year = "2024",

month = jul,

day = "26",

doi = "10.3934/ERA.2024209",

language = "English",

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pages = "4604--4613",

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AU - Lima, Mauricio F. S.

AU - Llibre, Jaume

PY - 2024/7/26

Y1 - 2024/7/26

N2 - The subject of this paper concerns with the bifurcation of limit cycles for a predator-prey model with small immigration. Since, in general, the biological systems are not isolated, taking into account immigration in the model becomes more realistic. In this context, we deal with a model with a Holling type I function response and study, using averaging theory of second order, the Hopf bifurcation that can emerge under small perturbation of the biological parameters.

AB - The subject of this paper concerns with the bifurcation of limit cycles for a predator-prey model with small immigration. Since, in general, the biological systems are not isolated, taking into account immigration in the model becomes more realistic. In this context, we deal with a model with a Holling type I function response and study, using averaging theory of second order, the Hopf bifurcation that can emerge under small perturbation of the biological parameters.

KW - Hopf bifurcation

KW - averaging equation

KW - limit cycle

KW - periodic orbit

KW - predator-prey system

UR - https://www.scopus.com/pages/publications/85201913591

U2 - 10.3934/ERA.2024209

DO - 10.3934/ERA.2024209

M3 - Article

SN - 1079-6762

VL - 32

SP - 4604

EP - 4613

JO - Electronic Research Announcements of the American Mathematical Society

JF - Electronic Research Announcements of the American Mathematical Society

IS - 7

ER -

Hopf bifurcation for a class of predator-prey system with small immigration

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