Transcritical bifurcation and Neimark-Sacker bifurcation of a discrete predator-prey model with herd behaviour and square root functional response

Autor:	Danyang Li, Xianyi Li
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	Predator-prey system with herd behaviour square root functional response semi-discretization method transcritical bifurcation Neimark-Sacker bifurcation Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Mathematical and Computer Modelling of Dynamical Systems, Vol 30, Iss 1, Pp 31-50 (2024)
Druh dokumentu:	article
ISSN:	13873954 1744-5051 1387-3954
DOI:	10.1080/13873954.2024.2304798
Popis:	ABSTRACTIn this paper, a discrete predator-prey model incorporating herd behaviour and square root response function is deduced from its continuous version by the semi-discretization method. Firstly, the existence and local stability of fixed points of the system are studied by applying a key lemma. Secondly, by employing the centre manifold theorem and bifurcation theory, the conditions for the occurrences of the transcritical bifurcation and Neimark-Sacker bifurcation are obtained. Not only that but the direction and stability conditions of the bifurcated closed orbits are also clearly shown. Finally, numerical simulations are also given to confirm the existence of Neimark-Sacker bifurcation.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/ff73cdf5636b44bca018733f4de2ada9 Zobrazit plný text záznamu View record in DOAJ